Solutions Key Exponents and Polynomials

CHAPTER 7 Solutions Key Exponents and Polynomials ARE YOU READY? PAGE 57. F. B. C. D 5. E 6. 7 7. 5 8. (-0 9. x 0. k 5. 9.. - -( - 5. 5. 5 6. 7. (- 6 (-(-(-(-(-(- 8 5 5 5 5 6 8. 0.06 9.,55 0. 5.6. 6 + p + + 9p 6 + + p + 9p 0 + p. 8y - x + y + 7x - x 8y + y - x + 7x - x 0y + x. ( + w - 5 + 6w - - 5w - 5 - + w + 6w - 5w + w. 6n - + 5n 6n + 5n - n - 5. no 6. yes; 8 9 9 7. yes; 6 6 6 8. no 9. yes: 00 0 0 0. yes;. yes;. no 7- INTEGER EXPONENTS, PAGES 60 65 CHECK IT OUT!. 5-5 5 5 5 5 5 - m is equal to _ 5 m. a. 0-0 0 0 0 0 0,000 b. (- - (- (-(-(-(- 6 _ c. (- -5 (- 5 (-(-(-(-(- - d. - -5 - - 5 - a. p - - _ 6 a. r 0 m - r 0 m - m c. _ g g _ h -6 h -6 g h 6 g h 6 m THINK AND DISCUSS. -; 0; t. EXERCISES GUIDED PRACTICE b. 8 a - b 0 8 (- - (6 0 8 (- 8 (-(- 8 b. r - 7 r - 7 r 7 7 r _. 0-7 0 7 0 0 0 0 0 0 0 _ 0,000,000 m 0-7 m is equal to _ 0,000,000 m.. 6 - _ 6 6 6 6 _. 0. - 5 - - - 5 5 5-5 Holt McDougal Algebra

5. - 6. -8 _ 7 8 7. - 8 - - - 8 8 8 8-5 _ 8. 0-0 0 0 00 9. (. 0 0. (- - (- (-(-(- - 7. -. b - (- - (- (-(- 9. (m - -5 (6 - -5-5 5 _ 6 6. m 0 m 0 7 8. 7 r -7 r -7 7 r 7 7 r 7 0. x 0 y - x 0 y - y y. _ c c _ d - d - c d c d. (t - (( - - _ _ 56 5. x 0 y - (7 0 (- - (- (-(-(- _ -6-7. k - k - k k 9. _ x 0 _ d - x 0. _ f - d - x 0 d x 0 d _ g -6 f - g -6 g 6 f g 6 f. p 7 q - p 7 q - p 7 q p 7 q PRACTICE AND PROBLEM SOLVING. - 5. 8 0 - oz is equal to oz. 6. 5-7. - 5 5 5 5 5 65 _ 8 _ 8. - 9 - - - 9 9 9-8 _ 9. - 6 - - - 6 6 6-6 0. 7 - _ 7 7 7 9. ( _. - 69. (- - _ (- (- -. (- (-(- 6 5. ( - 6. - 7 - - 8. ( v - ( (9-6 - 6 _ 6 6 6 _ 6 0. 0 m - n -5 _ ( _ _ - 7 7 _ 7. x - 5 0 - _ _ 56 9. (0 - d 0 (0-0 (- 0 0 (0 - (- -5 0 0 (- 5 0 0 _ (-(-(-(-(- - Holt McDougal Algebra

. (ab - ( ( (8 - - _. w v x v ( 0 (-5 0. k -. z -8 z -8 k z 8 z 8 5. - b _ 6. c - d c - d b - b d c b d c 7. -5 x - -5 x - -5 9. f 0 7 g 5. - -0 5 x x 7 f 0 _ g -0 7 g 0 _ g 0 7 _ s 5 s 5 _ t - t - s 5 t s 5 t 5. b 0 c 0 b 0 c 0 55. q - r 0 q - r 0 s 0 s 0 q q 8. x -6 y - x -6 y - 50. r -5 x 6 y _ x 6 y s - r -5 5. w -5 5. r 5 s s r 5 s - x -6 w -5 x 6 w 5 x 6 w 5 m - n 5 x -6 m - n 5 m n 5 n 5 m 56. a -7 b a -7 b c d - b a 7 _ b d a 7 c 57. h k - 6 m 58. z -5-5 5 _ c c d 6 h k - 6 h h 6 m k 60. (yz 0 ((-( 0 (- 0 6. (xy - - (((- - - (-6 - (-6 (-6(-6 6 6. (yz -x ((-( - (- - (- (-(-(- - 8 k m d - m 59. (x + y - ( + (- - - _ 6 6. (xyz - (((-( - (-6 - _ (-6-6 6. x -y -(- 65. xy - ((- - (- (-(-(-(- 66. Equation A is incorrect because 5 was incorrectly moved to the denominator. The negative exponent applies only to the base x. 67. a b - a b - a a b b 68. c - d c - d c d d c 5 Holt McDougal Algebra

69. v 0 w y - v 0 w y - w y w y 7. -5 y -6-5 y -6-5 - 5 y 6 y 6 7. _ a a _ b - b - 75. x -8 a b a b _ y 0 p - 76. - x -8 y x 8 y x 8 y - 0 5 q - 5 p - - p q q 70. ( a b -7 0 7. a -5 _ a -5 b -6 b 6 a 5 b 6 a 5 7. _ m m _ n - n - _ q - m n m n - p 77. Red blood cell: 5,000 - _ 5,000 White blood cell: (500-500 - _ 500 500 500 _ 50,000 _ 50,000 Platelet: (000-000 - 000 _ 000 000,000,000,000,000 78. always 79. never 80. sometimes 8. sometimes b -6 8. - ( 8 8 a n a -n _ - ( 9 9 _ 85. Possible answer: Look at the pattern below. As the exponent goes down by, the value is half of what it was before. 8,,, 0, -, - - 8 _ 86. - ; - 87. 9 - _ 9 9 9 8 ; 8 88. 6 _ 8 8 8 - ; 8 8 89. - ; 90. 7 - _ 7 7 7 9 ; 9 _ 9. 000 0 0 0 0 - ; - 0 9. - _ 6 6 ; 6 9. 5 5 - ; - 9a. fw v b. fw v fw f v f w v f w v f w v f - w v f - c. s s - TEST PREP 95. D; Since 0.0 5 _ 5 5 5 -, A, B, and 5 C are all equal and do not equal -5. 96. J 6 - _ 6 6 6, 8. never 8. sometimes 6 Holt McDougal Algebra

97. A a b - c - a b - a a c b b c c - 98. 5, or.5 - + (6 + 0 - + 8 0 + _ + + 5, or.5 99. a n; a -n a n and b 0 if b 0. So you have, or simply n a a n. CHALLENGE AND EXTEND 00. x - - - - 0 y x 6 8 8 6 Possible answer: y increases more rapidly as x increases. 0. n - - - - -5 n (- n - - - n ; (- n - if n is odd, and (- n if n is even. SPIRAL REVIEW 0. 6x - 8 + + 6x 6x 6 6 x 0. y 5-8 - + 8 _ +8 y 5 5 ( y - 5 5(- y -0 0. -9 (p - -9 (p + (- -9 p - + + -6 p -6 p - p 05..5h - 5 _ + 5 +5.5h 6 _.5h.5 6.5 h 06. w + 6 - w -0 6 - w -0 _ -6 _ -6 -w -6 -(-w -(-6 w 6 07. - n + - n - - n _ - - - - n -(- - ( - n 8 n 08. Independent variable: number of roses Dependent variable: total cost Let x represent the number of roses. f(x.50x 09. Independent variable: number of days Dependent variable: total cost Let x represent the number of days. f(x 0x + 0 0. y mx + b y x + (- y x -. y mx + b y 0x + y. y mx + b y x + 5. y - y m(x - x y - 5 -(x - y - 5 -x + + 5 _ + 5 y -x + 9 7- POWERS OF 0 AND SCIENTIFIC NOTATIONS, PAGES 66 7 CHECK IT OUT! a. 0-0.0 b. 0 5 00,000 c. 0 0 0,000,000,000 a. 00,000,000 0 8 b. 0.000 0 - c. 0. 0 - a. 85. 0 5 85,0,000 b. 0.6 0-0.006 a.,000 km. 0 5 km b.. 0 m/s,000 m/s 5. 5. 0 -, 0, 0 -, 0 -,.5 0 0,.5 0 List the numbers from least to greatest. 0 -, 0 -, 5. 0 -, 0,.5 0,.5 0 0 THINK AND DISCUSS..56 is not between and 0. 7 Holt McDougal Algebra

. EXERCISES GUIDED PRACTICE. A number written in scientific notation is a product with two parts: a decimal greater than or equal to and less than 0 and a power of 0.. 0 6,000,000. 0-5 0.0000. 0-0.000 5. 0 8 00,000,000 6. 0,000 0 7. 0.00000 0-6 8. 00,000,000,000,000,000 0 7 9. 650. 0 6 650,00,000 0. 8. 0-0.008. 9 0-0.09. 9.6 0 km 9,6,000,000,000 km. 8.5 0 -,.6 0 8, 5.85 0 -,.5 0 -, 8.5 0 8 List the numbers from least to greatest. 5.85 0 -,.5 0 -, 8.5 0 -,.6 0 8, 8.5 0 8 PRACTICE AND PROBLEM SOLVING. 0 000 5. 0-9 0.00000000 6. 0-0.00000000000 7. 0 00,000,000,000,000 8. 0.0 0-9.,000,000 0 6 0. 0.00000000000000 0-5. 9. 0 9,000..5 0-7 0.0000005. 0-5 0.000. 0.05 0 7 500,000 5. 0 0,000,000,000,000 6.,87,000,000.87 0 9 7.. 0 -,. 0,. 0 -,. 0,. 0 -,. 0 - List the numbers from least to greatest.. 0 -,. 0 -,. 0 -,. 0 -,. 0,. 0 8. Yes; the smallest diameter of a grain of pollen is. 0-5 m, which is greater than 0-7 m.,000,000 copies 9. 7 platinum 7,000,000 copies platinum 7,000,000.7 0 7 0. 0,080,000.008 0 7. 5,000.5 0 5. 70,000,000,000.7 0. 0.0000006 6 0-7. 0.000077 7.7 0-5 5. 0.0. 0-6. no; 5 0-7. yes 8. no;. 0 6 9. no;.5 0 0. no; 0 -. yes. no;.8 0. yes. The mass of an electron in scientific notation is 9. 0 - kg. Since the mass of the electron has a lower power of 0 than the mass of the proton and neutron, the electron has the least mass. 5a. 999:.9 0 8 90,000,000 000: 7. 0 8 70,000,000 00:.9 0 9,9,000,000 b. When you double 7. 0 8, you get approximately 0 8, or. 0 9 in scientific notation.. is close to., so Zorah s observation is correct. 6a. dam, hm, and km are larger than a meter since their powers of 0 are greater than and mm, cm, and dm are shorter than a meter since their powers of 0 are less than. b. 0 - _ 0 0 0 0 000 0.00 0-0 0 0 0.0 0-0 0 0. 0 0 0 0 0 00 0 0 0 0 000 7. 0-8. If the exponent is positive, move the decimal point that many places to the right. If the exponent is negative, move the decimal point that many places to the left. 9a. 0 8 00,000,000 b. Possible answer: It would be easy to accidentally omit a 0 or add an extra 0 when writing the number in standard form. You are probably less likely to make an error when using scientific notation. c. 0.00000068 6.8 0-7 TEST PREP 50. C;. 0 7,000,000 5. F; 8.5 8.5 0 5. C; Since 0.00000009.9 0-8, if,90,000,000.9 0 9 is removed, the list will be in order from least to greatest. 8 Holt McDougal Algebra

CHALLENGE AND EXTEND 5..7 GB 0 9 bytes GB MB 700 MB 0 6 bytes 700 700 7 About 7 times;.7 GB, the storage of the DVD, is the same as 700 MB, which is approximately 7 times 700 MB, the storage of the CD. 5a. ( 0 ( 0 0 0 6 0 0 600 0 600,000 6 0 5 b. ( 5 0 8 (.5 0-6 5.5 0 8 0-6 7.5 0 8 0-6 750,000,000 0-6 750 7.5 0 c. (. 0-8 ( 0 -. 0-8 0-8.8 0-8 0-0.000000088 0-0.000000000088 8.8 0 - d. (.5 0 - ( 0 6.5 0-0 6 5 0-0 6 0.000000000005 0 6 0.000005 5 0-6 e. First multiply the numbers, then multiply the powers of 0 by adding the exponents. f. Yes, but the answer 8 0 8, is not in scientific notation. After multiplying, you will have to rewrite the answer in scientific notation as.8 0 9. SPIRAL REVIEW 55. Let m represent the number of minutes. m 5 56. Let p represent the number of pounds. 0 p 8 57. Let m represent the amount of money spent. m > 50 58. x + y 8 + x - y x + 0 0 x 0 x 0 x 5 x + y 8 5 + y 8-5 -5 y (5, 60. -(x - 6y - + x + y -x + 8y 9 + x + y 0 + y y _ y y x - 6y - x - 6( - x - 6 - + 6 +6 x (, 6. (-8m 0 (-8(-5 0 (0 0 59. x + y - - (x + y - x + y - _ + (-x - y 0 - y - -y - _ -y - - - y x + y - x + - - - x - x - x - (-, 6. t - - _ 6 6. a - b 0 (5 - (6 0 5 _ 5 5 5 _ 5 _ 5 7- MULTIPLICATION PROPERTIES OF EXPONENTS, PAGES 7 80 CHECK IT OUT! a. 7 8 7 7 8 + 7 b. - 5 8 5 ( - ( 5 8 5 - + 5 8 + 5 0 9 Holt McDougal Algebra

c. m n - m ( m m n - m + n m 5 m 5 n n 60 min 60 s min 600 s. h h distance rate time d. x x - x - x - ( x x - ( x - x - x - x - - x 0 x -7 x 7 x 7 (.86 0 5 600 (.86 0 5 (.6 0 (.86.6 ( 0 5 0 6.696 0 8 Light travels about 6.696 0 8 mi in one hour. a. ( 5 5 0 c. ( a ( a - - a a a a 6 a + 6 a 8 b. ( -5 t - (- (-5 ( t 5 t 5 t c. ( x y ( x y - b. ( 6 0 6 0 6 0 a. (p p 6 p ( ( x ( y ( ( x - ( y - ( x y ( x (- y (- ( x 8 y ( x -8 y -6 ( x 8 x -8 ( y y -6 x 8-8 y x 0 y - y - y - 6 THINK AND DISCUSS. ( a a a 6, while a a a + a 5.. Product of Powers Property Multiplication Properties of Exponents Power of a Power Property Power of a Product Property EXERCISES GUIDED PRACTICE. + 5. n 6 n n 6 + n 8. 5 5 5 + 5 6. x x - x ( x x - x x - x x - x x - + x 5. distance rate time 000 ( 7.5 0 5 ( 0 ( 7.5 0 5 ( 7.5 ( 0 0 5 7.5 0 8 You would travel 7.5 0 8 mi in that time. 6. ( x 5 x 5 x 0 8. ( p p p 9 0. ( a - ( a 7 a - a 7 a - a - + a a. (t 5 5 t 5 t 5. ( r s 7 ( r 7 s 7 r 7 s 7 r s 7 6. - ( x 5 - ( ( ( x 5 - ( 8 x 5-8 x 5 7. ( y 8 y 8 y 9. ( - - - or, 8. xy ( x ( y xy x y xy x 6 y ( x x 6 (y y x + 6 y + x 7 y. (6k 6 k 6 k 5. ( - x 5 (- ( x 5-8 x 5-8 x 5 5 ( 6 ( 8 50 Holt McDougal Algebra

7. ( a b 5 ( a -5 ( ( a 5 ( b 5 ( a -5 ( a 5 b 5 a -5 ( a 0 b 0 a -0 ( a 0 a -0 b 0 a 0-0 b 0 a 0 b 0 b 0 b 0 PRACTICE AND PROBLEM SOLVING 8. ( + 0. a 5 a 0 a -5 a 5 a -5 a 5 a -5 a 5-5 a 0 9. 6 6 6 6 ( 6 6 ( 6 6 6 + 6 + 6 6 5 6 + 5 6 8. x 7 x -6 y - x 7-6 y - x x y. Area (.9 0 0 ( 5.5 0 (.9 5.5 ( 0 0 0 5.95 0 y.595 0 The area of Alaska is.595 0 ft.. ( 9, or 5 5. ( x - x (- x - x 7. b ( a ( b - b a b - b a b -6 ( b b -6 a b - 6 a b -5 a b 5 a a b 5. ( 6 0 6 0 0 6. ( b 6 b b 6 b b b b + b 5 8. ( x ( x - - x x x 8 x x 8 + x - (- 9. (x x 7 x. ( p q 7 ( p 7 ( q 7 p 7 q 7 p 8 q. - ( x - ( ( ( x - ( 56 x -56 x. ( x y (x y - 0. ( 5 w 8 5 ( w 8 5 w 8 5 w 6. ( - x ( ( x ( y ( x - ( y - ( x y ( x - y - ( x 9 y ( x - y -6 ( x 9 x - ( y y -6 x 9 - y - 6 x 7 y 6 5. a 0 a 6 + a 6 a ; 6 7. a 8 b a b ( a ( b ( a b ; 9. ( b - b (- b -8 b 8; 8. A lw ( x (x ( x x x + x (- ( x 56 x 56 x 6. a 8. a ( a ; a 9 b 8 a 9 b 8 a -9 b -8 a (- b 6 (- 0. a 6 ( a - ( b 6 - ( a b 6 - ; - a 0 + 6 a 0 a 6 ; 0. A bh ( a b ( b a ( b b a b + a b 5 Holt McDougal Algebra

. A bh ( ( m n ( (mn ( ( m ( n ( m n ( m n ( m n ( m 8 n ( m n ( ( m 8 m ( n n. x 6 y 5 m 8 + n + m 0 n 6 5. ( x ( x ( ( x ( ( x ( x ( 7 x ( x ( 7 x 9 ( 7 ( x x 9 08 x + 9 08 x 6. x y - x - y - ( x x - ( y - y - x - y - - x 0 y -6 y 6 y 6 7. ( 5 x ( 5 x ( 5 x + ( 5 x 5 ( x 5 x 5 x 6 9. a a 0 a ( ( a a 0 a ( a + 0 a ( a a a + a 6 5. 0 0-0 5 ( 0 0-0 5 0-0 5 0-0 5 0 - + 5 0, or 000 8. - ( x ( - x - ( x ( (- ( x - ( x ( x - ( x 8 ( x 8 - x 8 + 8 - x 6 50. (ab (ab - (ab - ab 5. ( x y ( x y - ( ( x ( y ( ( x - y - ( x y ( x - y - ( x y ( x - y - ( x x - ( y y - ( x - ( y - ( x 0 ( y ( ( y y 5. Earth: d rt (.86 0 5 500 (.86 0 5 ( 5 0 (.86 5 ( 0 5 0 9. 0 7 mi Mars: d rt (.86 0 5 760 (.86 0 5 ( 7.6 0 (.86 7.6 ( 0 5 0.6 0 7.6 0 8 mi Jupiter: d rt (.86 0 5 600 (.86 0 5 (.6 0 (.86.6 ( 0 5 0.86 0 8 mi Saturn: d rt 5. V lwh (.86 0 5 800 (.86 0 5 (.8 0 (.86.8 ( 0 5 0 8.98 0 8 mi ( a ( a 5 ( a b ( ( a a 5 a b 8 ( a + 5 a b 8 ( a 7 a b 8 a 7 + b 8 a 9 b The volume of the object is 8 a 9 b. 55a. Exponents are multiplied but should be added; x 6. b. Exponents are added but should be multiplied; x 0. c. Exponents should be multiplied; x 6. 5 Holt McDougal Algebra

56. ( - x ( 5 x - (- 5 ( x x - -5( x - -5( x - -5( x 5 - x 58. ( 6 w 5 ( v w 6 (6 ( v ( w 5 w 6 v w 5 + 6 v w 57. ( a b ( a b -6 ( a a ( b b -6 ( a + ( b - 6 a 7 ( b -5 a 7 ( a 7 b 5 59. ( m 7 ( m n ( 5 m n 8 ( 5 ( m 7 m m ( n n 8 5 ( m 7 + m n + 8 5 ( m 9 m n 9 5 m 9 + n 9 5 m n 9 60. ( b - ( b 5 ( b (- ( b 5 ( b - ( b 0 - + 0 b b 6 6. ( ( x 5 y ( ( ( x 5 y 6 ( x 5 y 6 x 5 y 6. (st t 5 6. (-t (-t ( - t -t ( (- t ( - t (- (- - ( t t t (- - ( t + t ( t t t + t 7 6. ( m ( m (8n ( m ( m ( 8 n ( 8 ( m m n (8 6 ( m + n 5 m 6 n b 5 ( s t t 5 9 s ( t t 5 9 s t + 5 9 s t 7 65a. Possible answer: Round -.0 to -. ( (- 9 79 b. Possible answer: Round 6.085 to 6 and round.89 to. ( 6 0 ( 0-5 (6 ( 0 0-5 0-0.0 66. speed ( 8.7 0 5 (. 0 ( 8.7 0 5 (. 8.7 ( 0 0 5 9.98 0 7.998 0 8 99,80,000 The speed of light is.998 0 8 m/s or 99,80,000 m/s. 67. Yes; because of the Commutative Property of Multiplication, they are both equal to x 6. 68. Number 6,000,000,000 (.9 0 (.6 0 0 (.9 0 (.6.9 ( 0 0 0.9 0 An adult has.9 0 cells. 69. (-k + k ( (- k + k 6 k + k 7 k 7. ( x + ( x ( ( x + ( x ( x + x x + x 6 x 7. (r s + 6 (rs + ( r s + 6 ( r s + r s + 6 r s + 0 r s + 7. (a b + (ab (b ( a b + ( a b (b 9 a b + ( ( a ( b b 9 a b + 6 a b + 9 a b + 6 a b 5 a b 7. ( x ( x ( x + x ( x + ( x + x ( x ( x + x x + + x x 6 + x 70. - z + (-z - z + ( (- z - z - 7 z -0 z 5 Holt McDougal Algebra

75a. Measure 600 0-9 ( 6 0 0-9 6 ( 0 0-9 6 0-7 600 nm is 6 0-7 m. b. v fw ( 5 0 ( 6 0-7 (5 6 ( 0 0-7 0 0 7 0 8 The speed of light is 0 8 m/s. c. Associative and Commutative Properties of Multiplication 76. c d c d (cd 78. 8 a b a b - 79. ( a b - ( a b k - m n ( k - m - n - ( k - m - n - ( kmn TEST PREP 80. C x x 0 x x 8. D n ( 0 5 ( 0 5 6 0 5 6 0 5 6. 0 6 CHALLENGE AND EXTEND 8. x 77. 6 a b + x 85. ( 6 a b (6ab 8. H ( 0 5 ( 0 ( ( 0 5 0 0 7. 0 8 8. F A bh (x(x ( (x x 6 x x x x 86. ( x y z ( x y z x y z x y z 88. (x + (x + - (x + - (x + - x + 90. ( x x x x x 9. (x y y x y y x y ( y x y 9 y x y 9. 7 7 x 7 7 + x 7 + x - - x 9 96. ( 6 x 6 6 6 x 6 6 6 x 6 6 x 6 x 6 x 8 97. (. 0 - m 0 cm m (. 0-0. ( 0-0. 0 0.. cm 87. (x + - (x + (x + - + x + 89. ( x y x z ( x y + z x x 9. ( x x x (y + z y + z x x x x x 9. 5 x 5 5 8 5 x + 5 8 x + 8 - - x 95. ( x x x x x x V s..78 The volume of the cube is.78 cm. SPIRAL REVIEW 98. DC ZY BC XY 75 x x 00 x _ 00 x 00 99. AB RS CB TS 8 5 x 8x 0 8x 8 _ 0 8 x 5 5 Holt McDougal Algebra

00. 5,, -, -7,... - - - The sequence appears to be an arithmetic sequence with a common difference of -. 5,, -, -7, -, -5, -9 - - - The next three terms are -, -5, -9. 0. -, -, 0,,... + + + This sequence is not an arithmetic sequence. 0. 0.,.0,.6,.,... +0.6 +0.6 +0.6 The sequence appears to be an arithmetic sequence with a common difference of 0.6. 0.,.0,.6,.,.8,.,.0 +0.6 +0.6 +0.6 The next three terms are.8,.,.0. 0. 7.8 0 6 7,800,000 0..95 0-0.00095 05. 98 0-98. 06. 0.06 0 8 6,000,000 7- DIVISION PROPERTIES OF EXPONENTS, PAGES 8 87 CHECK IT OUT! a. 9 c. 7 9-7 m 5 n m 5 n ( m 5 n m 0 n m 5-0 n - _ m -5 n n m 5 b. y y - y y - y d. 5 5 - - - 6 6 - _ 6 6 6. (. 0 6 ( 0 8. total debt number of people 6. 0 0 8. 0 6 0 8. 0 6-8. 0 -. 0.5 0 8 _. 0.5 0 8.8 0-8.8 0,800 The average debt per person was about $,800. a. ( ( ( 6 or 6, 8 c. _ ( a b ( a - b - a b ( a b - ( a 5a. ( c. ( s b a b - ( ( 9 _ 9 or 79, 6 - ( 9 s t - ( s ( t 9 s t s 9 s 9 t s 9 s t s b. _ ( a b c d b. ( _ a 5 ( a b 5 ( c d 5 a 5 ( b 5 ( c 5 ( d 5 a 5 b 0 c 0 d 5 b c - ( b c _ a ( b c (a ( b ( c a b 8 c 6 a 55 Holt McDougal Algebra

THINK AND DISCUSS. Possible answer: Both the Quotient of Powers Property and the Product of Powers Property require that the bases be the same. For quotients, you subtract the exponents. For products, you add the exponents. In the Power of a Quotient Property, each term is raised to the same power. In the Power of a Product Property, each factor is raised to the same power.. EXERCISES GUIDED PRACTICE. 5 8 5 8-6 5 6 5 5 _. - 9-5 9 5. _ 5 x 6-7 - 7 56 8 _ 56 8 5 5 x 6 5 x 6 x 6 x 6-6 x 0 5. (.8 0 ( 0 8. _ a 5 b 6 a 5 - b 6-7 a b 7 a b - a b.8 0 0 8 _.8 0 0 8 0.7 0-8 0.7 0 7 0 6. ( 5.5 0 ( 5 0 8 5.5 0 5 0 8 5.5 5 0 0 8. 0-8. 0-5 7. (.9 0 (.9 0 8..9 0.9 0.9.9 0 0 0-0 0 annual salary number of games 8. 0 6 6 _ 8. 6 0 6 0.05 0 6 50,000 The star baseball player makes $50,000 per game. 5 0. 5 ( x ( x - y - x y 5 ( x y - ( x y 9. (. a ( _ a ( a b ( ( a b _ a 6 b ( a ( a - 6 b - ( a - b - _ (. y 0 y y 0 - a b _ ( a b ( a ( b _ a 6 b y 9. ( x ( y x y 9 - ( 6 9 56 Holt McDougal Algebra

. ( x 5. ( - y - ( y x ( y (x _ y x _ y ( a 6 x b - ( 6. ( x - ( y y x ( y ( x y 8 x ( b a (b (a _ b a b 9 a b a PRACTICE AND PROBLEM SOLVING 7. 9 9-6 6 7 9. _ x 8 y x 8 - y - x y x 5 y 0 x 5 x 5 0. _ x 8 y x 8-9 y - z - x 9 yz x - y z - y xz. (.7 0 - ( 9. 0 8. 5 5 - - 5 5 5 75 - _.7 0 9. 0.7-0 9. 0 0.5 0 - - 0.5 0-6 5 0-7. ( 8. 0 9 ( 0-5. (. 0-5 ( 6 0-9 8. 0 0-5 8. 0 9 0-5. 0 9 - (-5. 0-5 _. 0 6 0 -. -5 0 6 0-0.7 0 0.7 0-7 0 -. (. 0 ( 8. 0 5. 0 5. Mass of Jupiter 6 0 0-6 8. 0 5-5 - (-. 8. 0 0 5 0.5 0-5 0.5 0 -.5 0-0 0 - - (- 0 0 7 The mass of Jupiter is 0 7 kg. 6. ( 6 8 8. _ ( a b 6 ( a - b - 6 a b ( a b - 6 ( a 6 b ( a 6 b 6 a b 6 7. ( a b ( a ( b a b 6 57 Holt McDougal Algebra

9. ( x y x y ( x - y - ( x - y ( y x y ( x y x 6 0. ( 7 - ( 7. (_ 8 w 7-6. ( - 7 ( 6x ( _ 6. x 6 x 6-5 x 5 6. _ x y a b x 8 w 7 w 7 7 - ( ( 7 6x 7 (6x _ 6 9 6 x 6 _ 9 6 x _ 96 9 x. ( 5 x -5 ( y 5 5 y x 5. 8 d 5 8 d ( y 5 5 ( x 5 y 5 x 0 d 5 d d 5 - d ( x 7. ( 6 x ( x 6 ( x _ 7 x 9 6 x 7 6 x 9 x x 9 - x 5 8. 5 ( x 5 x 5 0. ( a ( x 5 x _ 5 x 6 5 x 5 - x 6-5 x 5 x 0 a a ( a a. ( - p -5 p ( a a ( a - ( a - ( a ( a 7 a 6 - ( -5 p - p ( 5 p p (5 p - (5 p - ( p 5 5 p 5 p. _ ( b - ( b - - b ( b -5 b -0 b 0 9. _ ( c a ( c a a 5 ( a 5 ( c ( a a 0 _ c a 6 a 0 c a 6-0 c a - c a 58 Holt McDougal Algebra

. 0 ( 5 - ( 0 0-5 0 0 0 ( 0 - - ( 0-0 - 0 _ 00. _ ( x y - x y ( x - y - - ( x 0 y - ( y - (y - y - y ( - x 5. -( x (- ( x - x 8 _ x 8 - x 8 x 8 - x 8 - x 8-8 - x 0 -( - 6. x n x 0 x n x 0 - n x -n number of people 7. 000: area 9.7 0 6 8.8 0 _.8 9.7 0 8 0 6 0.00 0 8-6 0.00 0 0 number of people 8 995:.66 0 area 9.7 0 6 _.66 9.7 0 8 0 6 0.8 0 8-6 0.8 0.8 0 number of people 8 990:.8 0 area 9.7 0 6 _.8 9.7 0 8 0 6 0.65 0 8-6 0.65 0.65 0 8a. 0 - b. 0-7 - 0 c. 0-0 -7 0-7 - - (-7 0 0 5 The hydrogen ion concentration of lemon juice is 0 5, or 00,000 times greater than that of water. 9. Possible answer: The bases are the same, so subtract the exponent of the denominator from the exponent of the numerator: 5 6. When simplifying subtracting the exponents gives a 5, negative exponent: - 5 6. 50. x x 6 - x 6 5. a 8 b ( a ( b ( a 7 x ; 6 5. x x 7 - x x ; b 5. Let a represent the exponent of y and let b represent the exponent of x. ( x - y a y x b ( y a y x y a x x b y x b a ; b _ ; 5a. 589 nm 0-9 m nm 589 0-9 5.89 0-7 589 nm is 5.89 0-7 m. b. v fw 0 8 f ( 5.89 0-7 0 8 f ( 5.89 0-7 5.89 0-7 5.89 0-7 _ 5.89 0 8 f 0-7 0.509 0 8 - (-7 f 0.509 0 5 f 5.09 0 f The frequency of yellow light is about 5.09 0 Hz. TEST PREP 55. B ( 8 0 6 ( 0 _ 8 0 6 0 8 0 6 0 0 6-0 59 Holt McDougal Algebra

56. F (_ x x y 57. A (-x - ( x - y - - ( x y - - ( x y ( y x - ( y ( x ( y x _ 9 y 8 x _ x (- -(x - x 8 x -8 x - x x - x - - x 0 -( - CHALLENGE AND EXTEND 58. V lwh 0 x y (5xy(xh 0 x y (5 (x x(yh 59. 0 x y (5 x y h 0 x y (5 x y h 5 x y 5 x y x y x y h x - y - h x y h x x - (x - x - x - x + 60. _ (x + (x + - (x + (x + - x + 6. Statements Reasons. a m - n a m + (-n. Subtraction is addition of the opposite.. a m a -n. Product of Powers Property. a m a n. a m a n SPIRAL REVIEW. Definition of negative exponent. Multiplication can be written as division. 6. 6 6 6 6. 6. - 9-7 -7 65. 66. -(x - + x 5x + -(x - (- + x 5x + -x + + x 5x + + x 5x + - 5x _ -5x - x _ - - -x _ -x - - x - 67. x - - (x + 5x x - - (x - ( 5x x - - x - 5x -x - 5x _ +x _ +x - 8x - 8 8x 8 - x 68. + 5, or 70. ( t 5 ( t 5 6 t 5 6 t 0 69. k 5 k - k - ( k 5 k - k - k 5 - k - k k - k - k 0 7. - ( 5 x - 5 ( x -5 x -5 x 60 Holt McDougal Algebra

7-5 RATIONAL EXPONENTS, PAGES 88 9 CHECK IT OUT! a. 8 8 b. + 56 + 56 + 5 a. 6 6 b. 5 5 ( 6 ( 5 ( 6 8 c. 7 7 ( 7 a. x y ( 7 8 ( x y ( x ( y ( x ( y ( x ( y x y THINK AND DISCUSS ( 5. C 7 m 7(8 7 ( 8 7 ( 7 ( 7 7 9 The panda needs 9 Calories per day. ( x y b. 5 x 5 ( x y x ( x ( y ( x - ( x y ( x - ( x ( x - y x + (- y xy. Rewrite the expression as 5 to the power, all 0 raised to the power 5. Then simplify the exponent to _. Finally take the square root.. EXERCISES GUIDED PRACTICE. 5. 8 8. 6 6. 0 6 6 0 0 5. 7 7 6. 8 8 9 7. 6 6 6 8. 9 9 9. 65 65 5 0. 6 +. 8 + 6 6 + 8 + 6 6 + 7 + 8 0. 8 + 8. 5-8 + 8 5 - + 5 5 -. 8 ( 8 ( 8 7 6. 5 ( 5 ( 5 5 5 8. 6 ( 6 ( 6 6 6 0.. P a (6 ( 6 (8 The perimeter is m.. x y ( x y ( x ( y x y x y 5. x 6 y 6 ( x 6 y 6 ( x 6 ( y 6 x y x y 5 5. 8 ( 8 5 ( 8 5 5 7. 5 ( 5 ( 5 5 5 9. 6 ( 6 ( 6 56. 0 0 0 0. z ( z z z z 6. a b 6 ( a b 6 ( a ( b 6 a b a b 6 Holt McDougal Algebra

7. ( a a ( a ( a ( a ( a a a a + a ( z 9. z z ( z z z z z 8. ( x 0. 6 y ( x 6 ( y ( x ( y x y x y x 6 y 9 x ( _ x 6 y 9 x ( x 6 _ x x y ( y 9 x y PRACTICE AND PROBLEM SOLVING. 00 00 0. 5 5. 5 5 8. 79 79 7 5. 5 5 6. 96 96 _ 7. 56 8 8 56 8. 00 00 0 9. 5 + 8 0. 5-8 5 + 8 5-8 5 + 9 5 -. - 5. 56 + 0-5 56 + 0-8 + 0. (. 7 ( 7 8 5. 56 ( 56 6 7. 00 ( 00 5 9. 9 ( 9 5 0 000 5 9 5 6. 6 6 ( 6 6 5 5 5 8. ( 5 5 50. 5 ( 5 9 5. B 8 m 8 (6 ( 6 8 8 ( 8 (6 The mass of the mouse s brain is g. 5. a 6 c 9 ( a 6 c 9 ( a 6 ( c 9 a c a c 5. x 6 y ( x 6 y 6 ( x ( y x y x y 56. ( x y x ( x 58. ( y x x y 6 x x + y 6 x y 6 x y 6 x 6 y 6 y x ( _ x 6 y 6 y x 5. 8 m ( 8 m ( 8 ( m ( 8 m m 55. 7 x 6 ( x 6 ( y 6 y - x - ( x ( y ( y - ( x - x - y - x 0 y y ( a b 59. _ b ( a ( b _ b ( a 8 ( b ( b - a 8 b - a 8 b a 8 b ( 7 x 6 ( 7 ( x 6 ( 7 x x 57. ( a b b 6 ( a ( b ( b 6 ( a ( b ( b 6 a b b a b + a b a b 6 Holt McDougal Algebra

x 60. 56 ( 56 x x x 6. 5 x 5 ( x 5 x 5 x 5 5 x 5 5 x x x 6. 6 6 ( 6 x 6 x 6 x 66. 7 x 8 ( x x 7 x 8 7 ( 8 x 7 x x 68. ( _ 69 8 _ 8 69 8 70. ( _ 56 8 7. ( 6 9 7. ( 6 8 69 9 _ 56 8 56 8 ( 9 6 _ ( 9 6 ( 7 6 ( 6 8 ( _ 6 8 ( 8 7 6. x 5 5 ( x 5 5 x 6. x 6 0 6 ( x 6 0 6 x 0 65. x 5 ( x 5 x ( 5 x 5 x 65 x 67. 6 6 ( 6 x 6 6 x 6 x 69. ( 7 8 7. ( 6 7. ( 7 8 75. ( 9 _ 8 7 _ 8 7 6 _ 6 ( 8 7 ( _ 8 7 ( 9 ( 9 _ ( 9 ( 7 _ 8 76. ( 5 78. ( 6 7 ( 5 _ ( 5 ( 5 _ 8 5 7 6 _ ( 7 6 ( 9 6 77. ( 8 79. ( _ 5 8 ( 8 ( _ 8 ( 7 ( _ 8 5 ( 8 5 ( 5 _ 6 65 80. Lion: Wolf: L m 5 L m 5 ( 5 ( 5 ( 5 ( 5 ( 6 ( The lion s lifespan is 6 - years longer than the wolf s. 8. r 0.6 V 0.6(7 0.6 ( 7 0.6(.86 The radius is.86 in. 8. ( _ b _ b b b. Also, by definition ( b _ b. Therefore b b. 8. n will be less than n because <. n will be greater than n because >. 8. A is incorrect; the first line should be 6 _ ( 6. 85a. d ( 0.8 B L ( 0.8 ( 000 (0.8(5 (00 00 0 Distance to light source is 0 in. 6 Holt McDougal Algebra

b. d ( 0.8 B L ( 0.8 ( 000 8 (0.8(500 (00 00 0 Distance doubles to 0 in. 86. ( 6 8 ( 8 It is often easier to take the square root first so that the remaining numbers in the calculation are smaller. 87. B; 9 + 8 9 + 8 + 5 89. C; a 9 b ( a 9 b ( a 9 ( b a b a b CHALLENGE AND EXTEND 9. ( a ( a ( a 5 9. ( x ( x ( a a a 5 ( x ( x 9. y 5 ( y 5 5 5 y 5 5 5 y y ( 5 x + 8 x x + + 88. F; ( 8 90. H; 6 ( ( 8 which is not an integer 9. ( x 5 ( x 5 ( x ( x ( x + 5 9 95. 7 x 79 _ 7 x 7 _ 79 7 x x x 7 ( x 7 x 7 x x 96. 8 x (8 (8 8 x 8 x 8 ( x 8 x x x 97. S (π (V ( π ((6π ( π (08π π 08 π 08 π + ( 08 π 08 π ( 08 π 6 π ( 6 π 6 π 6π cm Both volume and surface area are described by 6π (although the units are different. SPIRAL REVIEW 98. x + 6 Case x + 6-6 - 6 x - 99. 5x + 5 0 5x + 5 0 _ - 5-5 5x -5 5x 5-5 5 x - 00. x - Case x - + + x x x Case x + 6 - - 6-6 x -8 Case x - - + + x - x - x - 6 Holt McDougal Algebra

0. n + 5 < - 5-5 n < 9 n < 9 n < 0. x + - _ - x ( ( x x 0. 7 y + _ - _ - - y - y - y 0. domain: {x x } range: {y y,, 5, 6} not a function 05. domain: {x x -, -, 0, } range: {y y 0,,, } function 06. domain: {x x 5, 7, 9, } range: {y y } function READY TO GO ON? PAGE 95. t -6-6 6 6. r 0 s - 8 0 0-0 0 0 _ 00 5. x x y -6 y -6 x y 6 x y 6 07. domain: {x x } range: {y y } function. n - (-5 - (-5 (-5(-5(-5-5 -_ 5. 5 k - 5 k - 5 k 5 k 6. 8 f - g 0 8 f - g 0 8 f 8 f 7. _ a - _ b - a - b a b a b - _ 8. 0-0 0 0 0 000 0.00 0-0 0 0 0.0 0-0 0 0. 0 0 0 0 0 00 0 0 0 0 000 9. 0 0,000 0. 0.000000 0-7. 00,000,000,000 0. 8. 0 8,000. 0.5 5 0 -. 5 + 5 7, or 8 6. p p 5 p + 5 p 9 8..5 (.8 0 0 5. 5-5 -, or 9 7. a a -6 a - ( a a -6 a - a - 6 a - a - a - a - - a -5 a 5 (.5.8 0 0 7 0 0 70,000,000,000 The swarm of locusts weighs 7 0 0 g or 70,000,000,000 g. 9. ( x ( x 7 x 7 x. ( - d 7 (- ( d 7 6 d 7 6 d 0. ( m n 5 ( m 5 ( n 5 m 5 n 5 m 5 n 0 65 Holt McDougal Algebra

. ( c d 6 ( c 5 d ( c ( d 6 (( c 5 ( d ( c d 6 ( c 5 d ( c d 8 ( c 0 d ( c c 0 ( d 8 d c + 0 d 8 + c d. _ a 5. 6 9 5. ( 6 7 6 9-7 6 6 5 6. _ ( p 5 _ 7 5 p q ( p - q - ( p q - ( p q ( p ( q _ ( p q 8 p q 8 7. ( 8 0 9 ( 0 6 _ 8 0 9 8 8. (.5 0 5 ( 7 0 8 a a 5-0 6 a 0 9 0 6 0 9-6 0 5.5 0 7 0 8.5 7 0 5 0 8 0.5 0 5-8 0.5 0-5 0-9. ( 0 ( 0 _ 0 0. 8 8 9 0 0 0 0.5 0-0.5 0 0.5 0 -. 5 5 5. 6 8. 0 9 0. x 8 y ( x 8 y ( x 8 ( y ( x 8 ( y ( x ( y x y 5. r 9 ( r 9 r 9 r z ( z 6 z 6 z 6. 6 7. p q ( p q ( p ( q ( p ( q ( p ( q p q 7-6 POLYNOMIALS, PAGES 96 50 CHECK IT OUT! a. The degree is. b. The degree is. c. The degree is. a. 5x: degree -6: degree 0 The degree of the polynomial is. b. x y : degree 5 x y : degree 5 - x : degree : degree 0 The degree of the polynomial is 5. a. 6 - x + x 5 + 9 x x 5 + 9 x - x + 6 The leading coefficient is. b. 8 y 5 - y 8 + y - y 8 + 8 y 5 + y The leading coefficient is -. a. Degree: Terms: x + x -x + is a cubic polynomial. b. Degree: 0 Terms: 6 is a constant monomial. c. Degree: 8 Terms: - y 8 + 8 y 5 + y is an 8th-degree trinomial. 66 Holt McDougal Algebra

5. -6 t + 00t + 6-6 (5 + 00(5 + 6-6(5 + 00(5 + 6-00 + 000 + 6 606 When the firework explodes, it will be 606 ft above the ground. THINK AND DISCUSS. Possible answer: x + x - contains an expression with a negative exponent. - a contains a variable within a denominator. b. EXERCISES GUIDED PRACTICE. d. c. a. The degree is 0. 5. The degree is. 6. The degree is 8. 7. The degree is 0. 8. x : degree -x: degree : degree 0 The degree of the polynomial is. 9. 0.75 a b: degree a b 5 : degree 8 The degree of the polynomial is 8. 0. 5y: degree -8 y : degree 00: degree 0 - y : degree The degree of the polynomial is.. r : degree r : degree -5: degree 0 The degree of the polynomial is.. a : degree a : degree -a: degree The degree of the polynomial is.. k : degree k : degree - k : degree k: degree The degree of the polynomial is.. -b + 5 + b b - b + 5 The leading coefficient is. 5. 9 a 8-8 a 9-8 a 9 + 9 a 8 The leading coefficient is -8. 6. 5 s - s + - s 7 - s 7 + 5 s - s + The leading coefficient is -. 7. x + x - x + x - The leading coefficient is. 8. 5g - 7 + g g + 5g - 7 The leading coefficient is. 9. c + 5 c + 5 c - 5 c + 5 c + c - The leading coefficient is 5. 0. Degree: Terms: x + x + is a quadratic trinomial.. Degree: Terms: x - 7 is a linear binomial.. Degree: Terms: 8 + k + 5 k is a quartic trinomial.. Degree: Terms: q + 6 - q + q is a quartic polynomial.. Degree: Terms: 5 k + 7 k is a cubic binomial. 5. Degree: Terms: a + a - a is a quartic trinomial. 6.. r +.rl. (6 +.(6(0.(6 +.(6(0.0 + 88. 0. The surface area of the cone is approximately 0. cm. PRACTICE AND PROBLEM SOLVING 7. The degree is. 8. The degree is. 9. The degree is 6. 0. The degree is 0.. The degree is 7.. The degree is 5.. The degree is.. The degree is 0. 5. a : degree a : degree -6a: degree The degree of the polynomial is. 6. b: degree -5: degree 0 The degree of the polynomial is. 7..5 y : degree -.y: degree -6: degree 0 The degree of the polynomial is. 8. -5 f : degree f 6 : degree 6 0 f 8 : degree 8 The degree of the polynomial is 8. 9. n : degree -n: degree The degree of the polynomial is. 0. r : degree r 6 : degree 6 The degree of the polynomial is 6...5 +.9 t - t + t.9 t - t + t +.5 The leading coefficient is.9.. 8a - 0 a + -0 a + 8a + The leading coefficient is -0.. x 7 - x + x - x 5 + x 0 x 0 + x 7 - x 5 + x - x The leading coefficient is. 67 Holt McDougal Algebra

. -m + 7 - m - m - m + 7 The leading coefficient is -. 5. x + 5x - + 5 x 5 x + x + 5x - The leading coefficient is 5. 6. -n + - n - n - n + The leading coefficient is -. 7. d + d - d + 5 - d + d + d + 5 The leading coefficient is -. 8. s + s + 6 s + s + 6 The leading coefficient is. 9. x - x 5 - x + - x 5 - x + x + The leading coefficient is -. 50. Degree: 0 Terms: is a constant monomial. 5. Degree: Terms: 6k is a linear monomial. 5. Degree: Terms:.5 x -.x - 6 is a cubic trinomial. 5. Degree: Terms: g + g - is a quadratic trinomial. 5. Degree: Terms: x - 6x is a quadratic binomial. 55. Degree: Terms: 6 - s - s is a quartic trinomial. 56. Degree: Terms: c + 7 - c is a cubic trinomial. 57. Degree: Terms: - y is a quadratic monomial. 58..675v + 0.096 v.675(0 + 0.096 (0.675(0 + 0.096(900 0.5 + 86. 96.65 The stopping distance of a car traveling at 0 mi/h is 96.65 ft. 59. always 60. sometimes 6. never 6. sometimes 6a. c - 9 c + 9.5c ( - 9 ( + 9.5( ( - 9( + 9.5( - 9 + 9.5 58.5 The volume of the box when c in. is 58.5 in. b. c - 9 c + 9.5c (.5-9 (.5 + 9.5(.5 (.75-9(.5 + 9.5(.5.5-87.75 + 0.5 66 The volume of the box when c.5 in. is 66 in. c. c - 9 c + 9.5c (.5-9 (.5 + 9.5(.5 (76.765-9(8.06 + 9.5(.5 07.06-70.8 + 97.75 0 The volume of the box when c.5 in. is 0 in. d. Yes; the width of the cardboard is 8.5 in., so.5 in. cuts will meet, leaving nothing to fold up. Polynomial x - x 0 x 5 6. 5x - 6-6 -6 9 65. x 5 + x + x -8 0 70 66. -0 x -0 0-50 67. Possible answer: x + x - 6 68. Possible answer: 5x - 69. Possible answer: 5 70. Possible answer: 6 x 7. Possible answer: x 5-7. Possible answer: x - x + 5 7. Possible answer: First identify the degree of each term. From left to right, the degrees are, 0,,, and. Arrange the terms in order of decreasing degree, and move the plus or minus sign in front of each term with it: - x + x + 5 x - x -. 7a. x: degree 6: degree 0 The degree of the polynomial is. 7b. 8 x : degree x: degree The degree of the polynomial is. 75. A is incorrect. The student incorrectly multiplied - by - before evaluating the power. TEST PREP 76. C; A has degree 8, B has degree, C has degree 0, and D has degree. So C has the greatest degree. 77. J - x + x - 5x + 7 -(- + (- - 5(- + 7 -(- + ( - 5(- + 7 + + 5 + 7 9 78. Time (s Height (ft 59 86 8 The rocket will be the highest after s. 68 Holt McDougal Algebra

CHALLENGE AND EXTEND 79a. 0.06 m - 0.90 m +.56m + 50.0 0.06 ( - 0.90 ( +.56( + 50.0 0.06(8-0.90( +.56( + 50.0 0.8 -.56 + 9. + 50.0 58 0.06 m - 0.90 m +.56m + 50.0 0.06 (5-0.90 (5 +.56(5 + 50.0 0.06(5-0.90(5 +.56(5 + 50.0-9.75 +.8 + 50.0 65 The average length of a two-month-old baby boy is 58 cm and the average length of a five-month-old baby boy is 65 cm. b. 0.06 m - 0.90 m +.56m + 50.0 0.06 (0-0.90 (0 +.56(0 + 50.0 0.06(0-0.90(0 +.56(0 + 50.0 0-0 + 0 + 50.0 50.0 The average length of a newborn baby boy is 50.0 cm. c. The first three terms of the polynomial will equal 0, so just look at the constant. 80a. x 5 + x b. yes; 0 < x < ; raising a number between 0 and to a higher power results in a lesser number. So if x is between 0 and, the bionomial with the least degree will have the greatest value. SPIRAL REVIEW 8. 90 - m 8. 0.50p 8. y -x + 5 y -x + 5 x + y y -x + This system is inconsistent. It has no solution. 8. x + 8y 0 y - x + 5 y -x + 5 y - x + 5 This system is consistent and dependent. It has infinitely many solutions. 85. This system is consistent and independent. It has one solution. 86. 7 7 -, or 6 87. _ x 6 y x 6 - y - 9 x y 9 x y -5 x y 5 88. _ ( v 5 ( v - w -5 v w ( v w -5 ( v w 5 ( v ( w 5 ( v v 6 w 0 _ w 0 89. ( p - ( p p - - ( p - - ( p - ( p ( p p 8 6 7-7 ADDING AND SUBTRACTING POLYNOMIALS, PAGES 50 509 CHECK IT OUT! a. s + s + s 5 s + s c. x 8 + 7 y 8 - x 8 - y 8 x 8 - x 8 + 7 y 8 - y 8 x 8 + 6 y 8 d. 9 b c + 5 b c - b c b c b. z - 8 + 6 z + z + 6 z - 8 + 0 z - 6. (5 a + a - 6a + a + ( 7 a - 0a (5 a + 7 a + ( a + a + (-6a - 0a a + 5 a - 6a. ( x - x + - ( x + x + ( x - x + + ( - x - x - ( x - x - x + (-x + ( - - x - x. (-0.0 x + 5x - 500 _ + (-0.0 x + x - 700-0.05 x + 6x - 00 69 Holt McDougal Algebra

THINK AND DISCUSS. - x and -9 x ; -.7y and y; 5 x y and 5 x y. Take the opposite of each term: -9 t + 5t - 8.. EXERCISES GUIDED PRACTICE. 7 a - 0 a + 9a - a + 9a. 0.07 r + 0. r + 0.9 r 0.07 r + 0.9 r + 0. r 0.6 r + 0. r. p + p p 6. -8m + 5-6 + m -8m + m + 5-6 m - 7. (5 n + n + 6 + (8 n + 9 (5 n + 8 n + n + (6 + 9 n + n + 5. x + 9 y - 6 x x - 6 x + 9 y 7 x + 9 y 5. 5 b c + b c - b c b c 8. (.7 q - 8q +.7 + (. q -.9q +.6 (.7 q +. q + (-8q -.9q + (.7 +.6 8 q - 0.9q + 5. 9. (-x + + (9 x + x - 8 9 x + (-x + x + ( - 8 9 x - x - 6 0. (9 x + x + ( x + 6 x - 8 x + x (9 x + x - 8 x + ( x + 6 x + x x + 8 x. (6 c + 8c + 6 - ( c (6 c + 8c + 6 + ( - c ( 6 c - c + 8c + 6 c + 8c + 6. (6 y - 8y + 9 - (6 y - y + 7y (6 y - 8y + 9 + (-6 y + y - 7y (6 y - 6 y + (-8y + y - 7y + 9 0 y - y + 9. (r + 5 - (5r - 6 (r + 5 + (-5r + 6 (r - 5r + (5 + 6 -r +. (-7 k + - ( k + 5k - (-7 k + + (- k - 5k + ( -7 k - k + (-5k + ( + -9 k - 5k + 5. m ABD (8 a - a + 5 + (7a + 8 a + (-a + 7a + (5 + 8 a + 5a + 9 PRACTICE AND PROBLEM SOLVING 6. k + 6 k + 9 k k + 9 k + 6 k k + 6 k 7. 5m + n + 6n - 8m 5m - 8m + n + 6n n + 6n - m 8..5 a - 8. b -.6 b.5 a -.7 b 9. d 5 + - d 5 d 5 - d 5 + d 5 + 0. 7xy - x y - xy 7xy - xy - x y - x y + 5xy. -6 x + 5x + x + x -6 x + x + x + 5x 5x. x + x + x + x x + x + x + x x + x. b - b - - b - b b - b - b - b - b - b - 5. ( t - 8t + (8 t + 9t ( t + 8 t + (-8t + 9t 0 t + t 6. (-7 x - x + + ( x - 9x (-7 x + x + (-x - 9x + - x - x + 7. ( x 5 - x + ( x + x ( x 5 + x + (-x + x x 5 + x. x - - x - x - x - - x - 5 8. (- z + z + z + z + ( z - 5 z (- z + z + z + ( -5 z + (z + z z - 5 z + z 9. ( t + 8 t - ( t ( t + 8 t + ( - t ( t - t + 8 t - t + 8 t 70 Holt McDougal Algebra

0. ( x - x - ( x + x - x ( x - x + (- x - x + x ( x - x + (-x - x + x x - x. (5m + - ( 6 m - m (5m + + (-6 m + m -6 m + m + 5m +. ( s + s - (-0 s + 6s ( s + s + ( 0 s - 6s ( s + 0 s + (s - 6s s - s. width (6 w + 8 - ( w - w + (6 w + 8 + (- ( w - (-w - ( (6 w + 8 + (- w + 6w - ( 6 w - w + 6w + (8 - w + 6w +. P l + w (a + b + (7a - b (a + (b + (7a + (-b 8a + 6b + a - b 8a + a + 6b - b a + b 5. (t - 7 + (-t + (t - t + (-7 + t - 5 7. (n - - n (n - + (-n (n - n + (- n - 9. ( x + x - 6 + ( x - x + 5 6. ( m + m + ( - m ( m - m + m m + m 8. (-v - 7 - (-v (-v - 7 + (v (-v + v + (-7 v - 7 ( x + x + (x - x + (-6 + 5 6 x - x - 0. ( z - z - + ( z - 7z - ( z + z + (-z - 7z + (- - z - 0z -. (5 u + u + 7 - ( u + u + (5 u + u + 7 + ( - u - u - ( - u + ( 5 u - u + u + (7 - - u + u + u + 6. (-7 h - h + 7 - (7 h - h + (-7 h - h + 7 + (-7 h + h - ( -7 h - 7 h + (-h + h + (7 - - h -. P l + w 5 (x + + (x + 7 5 (x + ( + (x + (7 5 x + 6 + 6x + 5 x + 6x + 6 + 5 0x + 0 _ -0 _ - 0 5 0x 5 0 _ 0x 0 x, or x.5. Yes; the simplified form of both expressions is 5 m + m - 0. No; the simplified form of the original expression is -9 m - m + 0 and the simplified form of the new expression is -9 m + m - 0. 5. B is incorrect. The student incorrectly tried to combine 6 n and - n, which are not like terms, and tried to combine n and 9n, which are not like terms. Polynomial Polynomial Sum 6. x - 6 x - 0x + x - 0x - 7. x + 5 x + 6 5x + 8. x - x - 9 5 x + 8 6 x - x - 9. 7 x - 6x - 6x + 7 x + 50. x + 5 x 7 x - 5 x + 9 x + 5. x + x - 5 x + x + 6 x + x + 5. No; polynomial addition simply involves combining like terms. No matter what order the terms are combined in, the sum will be the same. Yes; in polynomial subtraction, the subtraction sign is distributed among all terms in the second polynomial, changing all the signs to their opposites. 5a. b. P l + w (x + + (x - (x + ( + (x + (- x + 8 + x - 6 x + x + 8-6 x + c. P x + (5 + 60 + 6 He will need 6 ft of fencing. TEST PREP 5. C; Since - y + 9 y + y - y, and -, the term must be in the form ay. So -y + ay - 6y -5y gives - + a - 6-5 or a. So the missing term is y. 7 Holt McDougal Algebra

55. G; Since t - t - (-7t - t t + 6t -5 t - t, G is correct. 56a. P l + w - (x - + (x + - (x + (- + (x + ( - x - + x + 8 - x + x - + 8-6x + b. 6x + 50 - - 6x 7 6x 6 7 6 x 7.8 7; If x 7, Tammy will need 6(7 + 5 feet of wallpaper border. However, if x 8, Tammy will need 6(8 + 5 feet of wallpaper border, which is more than the store has. c. (x - ft (x + ft ((7 - ft (7 + ft ft ft CHALLENGE AND EXTEND 57. P b + s _ - s - s P - s b b ( x + x + 8 - ( x + 5 ( x + x + 8 + (- x - (5 ( x + x + 8 + ( - x - 0 ( x - x + x + (8-0 x - 58. Possible answer: m + m, m + m 59. Possible answer: 5 m + m, m - m 60. Possible answer: m + m, m + m + m + m 6. Possible answer: m + m 66. x + y 8 _ -x _ -x y -x + 8 Plot (0, 8. Count units down and unit right and plot another point. Draw the line connecting the two points. 67. y x + 6 x + 6 y y x + Plot (0,. Count unit up and units right and plot another point. Draw the line connecting the two points. 68. y (-x + y (-x + ( y -x + Plot (0,. Count units down and unit right and plot another point. Draw the line connecting the two points. 6. Possible answer: m + m + m, m + m + m, m - m + m SPIRAL REVIEW 6. d + 5 - - 5-5 d -7 6. 5 < m - _ + + 6 < m m > 6 65. -6 + t < -6 +6 +6 t < 0 69. b b 7 b + 7 b 7. ( - z 6 (- ( z 6 9 z 6 9 z 70. c d ( c -5 c d c -5 c d c -5 ( c c -5 d c - 5 d c - d d c d c 7 Holt McDougal Algebra

7. ( j k -5 ( k ( ( j ( k -5 ( k ( j k -5 k ( j 9 k -5 k 8 j 9 ( k -5 k 8 j 9 k -5 + 8 j 9 k -7 j 9 k 7 j 9 k 7 7-8 MULTIPLYING POLYNOMIALS, PAGES 5 59 CHECK IT OUT! a. ( x ( 6 x ( 6 ( x x 8 x 5 c. ( x y ( x z ( y z 5 ( ( x x (y y ( z z 5 x 5 y 5 z 7 a. ( x + x + ( x + (x + ( 8 x + x + 6 b. ab (5 a + b ab ( 5 a + ab(b ( 5 ( a a (b + ((a(b b 5 a b + a b b. ( r t ( 5 t ( 5 ( r ( t t 0 r t c. 5 r s (r - s 5 r s (r + 5 r s (-s (5 ( r r ( s + (5 (- ( r ( s s 5 r s - 5 r s a. (a + (a - a(a + a(- + (a + (- a - a + a - a - a - b. (x - (x - (x - x(x + x(- - (x - (- x - x - x + 9 x - 6x + 9 c. ( a - b (a + b a(a + a ( b - b (a - b ( b a + 8a b - a b - b a + 7a b - b a. (x + ( x - x + 6 x ( x - x + 6 + ( x - x + 6 x ( x + x(-x + x(6 + ( x + (-x + (6 x - x + 6x + x - x + 8 x - x - 6x + 8 b. (x + ( x - x + 5 x ( x - x + 5 + ( x - x + 5 x ( x + x(-x + x(5 + ( x + ( -x + (5 x - 6 x + 5x + x - x + 0 x - x + x + 0 5a. Let x represent the width of the rectangle. A lw (x - (x x(x - (x x - x The area is represented by x - x. b. A x - x (6 - (6 6 - The area is m. THINK AND DISCUSS. Possible answer: Both numbers and polynomials are set up in two rows and require you to multiply each item in the top row by an item in the bottom row. In the end, you add vertically to get the answer. When you are multiplying polynomials, the items are monomial terms. When your are multiplying numbers, the items are digits.. EXERCISES GUIDED PRACTICE. ( x ( 7 x ( 7 ( x x x 6. ( -5m n ( m n (-5 ( m m ( n n -0 m n 5 7 Holt McDougal Algebra

. ( 6r s ( s t ( ( 6 r t ( r r ( s s ( t t r 5 s 5 t 5. ( a 5 (a ( ( a 5 a a 6 5. (- x y (-7 x y (- (-7 ( x x ( y y x 7 y 6. (-p q (5 p q (- q (- 5 (- (p p ( q q q 0 p q 9 7. ( x + x + ( x + (x + ( x + 8x + 8. ab ( a + b ab ( a + ab ( b ( ( a a (b + ( (a ( b b 6 a b + 9a b 9. a b ( a b + a b a b ( a b + a b ( a b ( ( a a (b b + ( ( a a ( b b 6 a 5 b + a b 0. -x ( x - x + 6 -x ( x - x(-x - x(6 - x + x - 8x. 5 x y (x y - y 5 x y (x y + 5 x y(-y (5 ( x x (y y + (5 (- ( x (y y 0 x y - 5 x y. 5 m n m n (m - n (5 ( m m ( n n (m - n 5 m n 5 (m - n 5 m n 5 (m + 5 m n 5 (-n (5 ( m m ( n 5 + (5 (- ( m ( n 5 n 0 m n 5-5 m n 6. (x + (x - x(x + x(- + (x + (- x -x + x - x - x -. (x + (x + (x + x(x + x( + (x + ( x + x + x + x + x + 5. (x - (x - (x - x(x + x(- - (x - (- x - x - x + x -x + 6. (y - (y - 5 y(y + y(-5 - (y - (-5 y - 5y - y + 5 y - 8y + 5 7. ( a - b ( a - b a (a + a ( - b - b(a - b ( - b a - ab - a b + 6 b 8. ( m - mn (mn + n m (mn + m ( n - mn(mn - mn ( n m n + m n - 6 m n - m n m n - 5 m n - m n 9. (x + 5 ( x - x + x ( x - x + + 5 ( x - x + x ( x + x(-x + x( + 5 ( x + 5(-x + 5( x - x + x + 5 x - 0x + 5 x + x - 7x + 5 0. (x + ( x - 5x + x ( x - 5x + + ( x - 5x + x ( x + x(-5x + x( + ( x + (-5x + ( x - 5 x + 6x + x - 0x + 8 x - x - x + 8. (x - (- x + x - 5 x (- x + x - 5 - (- x + x - 5 x ( - x + x(x + x(-5 - ( - x - (x - (-5-6 x + x - 0x + x - 8x + 0-6 x + x + x - 8x + 0. (-x + 6 ( x - x + -x ( x - x + + 6 ( x - x + -x ( x -x ( - x -x( + 6 ( x + 6 ( - x + 6( -8 x + x - x + x - 6 x + 6-8 x + 6 x - 6 x - x + 6 7 Holt McDougal Algebra

. (x - 5 ( x + x + x ( x + x + - 5 ( x + x + x ( x + x(x + x( -5 ( x - 5(x - 5( x + x + x - 5 x - 5x - 5 x - x - x - 5. (a + b(a - b(b - a (a(a + a(-b + b(a + b(-b (b- a ( a - ab + ab - b (b - a ( a - b (b - a a (b + a (-a - b (b - b (-a a b - a - b + a b - a + a b + a b - b 5a. A lw (x - (x x(x - (x x - x The area is represented by x - x. b. A x - x ( - ( (6 - ( - 0 The area is 0 in. PRACTICE AND PROBLEM SOLVING 6. ( x ( 8 x 5 ( 8 ( x x 5 x 7 7. ( - r s ( 6 r s (- 6 ( r r ( s s - r 5 s 5 8. (5x y ( x z ( y z ( 5 ( x x ( y y ( z z 5 x y 5 z 7 9. ( - a (-5a (- (-5 ( a a 0 a 0. (6 x y (- x y (6 (- ( x x ( y y - x 5 y. ( - a b ( - b ( - a b (- (- (- ( a a ( b b b -6 a 5 b 6. ( 7 x (x y 5 ( x y (7 ( x x x ( y 5 y x 6 y 7. ( - a b c ( a b c ( a b c 5 (- ( a a a ( b b b ( c c c 5 - a 7 b 7 c 8. ( m n ( m n (mn ( ( m m m ( n n n m n 5. 9s(s + 6 9s(s + 9s(6 9 s + 5s 7. x ( 9 x - x x ( 9 x + x(-x 7 x - x 6. 9 ( x - 5x 9 ( x + 9(-5x 8 x - 5x 8. ( x + 5x + ( x + (5x + ( 6 x + 5x + 9. 5 s t ( s - t 5 s t (s + 5 s t ( - t (5 ( s s ( t + (5 (- ( s ( t t 0 s t - 5 s t 5 0. x y 5 x y (6x + y (5 ( x x ( y y (6x + y 5 x y (6x + y 5 x y (6x + 5 x y ( y (5 6 ( x x ( y + (5 ( x ( y y 0 x 5 y + 5 x y 6. -5x ( x - x - -5x ( x - 5x(-x - 5x(- -0 x + 5 x + 5x. - a b ( a b - a b - a b ( a b - a b ( - a b (- ( a a ( b b - ( - ( a a ( b b -6 a b 5 + a b. -7 x y x y (x - y (-7 ( x x (y y (x - y -7 x 5 y (x - y -7 x 5 y (x - 7 x 5 y (-y (-7 ( x 5 x ( y + (-7 (- ( x 5 ( y y - x 6 y + 7 x 5 y. (x + 5(x - x(x + x(- + 5(x + 5(- x - x + 5x - 5 x + x - 5 5. (x + (x + (x + x(x + x( + (x + ( x + x + x + 6 x + 8x + 6 75 Holt McDougal Algebra

6. (m - 5 (m - 5(m - 5 m(m + m(-5-5(m - 5(-5 m - 5m - 5m + 5 m - 0m + 5 7. (5x - (x + 5x(x + 5x( - (x - ( 5 x + 5x - x - 6 5 x + x - 6 8. (x - (x - (x - x(x + x(- - (x - (- 9 x - x -x + 6 9 x - x + 6 9. (5x + (x - 5x (x + 5x (- + (x + (- 0 x - 5x + x - 0 x - x - 50. (x - (x - x(x + x(- - (x - (- x - x - x + x - x + 5. (x - 8(7x + x(7x + x( - 8(7x - 8( 7 x + x - 56x - 7 x - 5x - 5. (x + 7(x + 7 x(x + x(7 + 7(x + 7(7 6 x + x + x + 9 6 x + 5x + 9 5. (x + ( x - x + 5 x ( x - x + 5 + ( x - x + 5 x ( x + x(-x + x(5 + ( x + (-x + (5 x - x + 5x + x - 6x + 0 x - x - x + 0 5. (x + 5 ( x - x + x ( x - x + + 5 ( x - x + x ( x + x(-x + x( + 5 ( x + 5(-x + 5( x - 8 x + 6x + 5 x - 0x + 5 x - x - x + 5 55. (5x - (- x + x - 5x (- x + x - - (- x + x - 5x ( - x + 5x(x + 5x(- - ( - x - (x - (- -0 x + 0 x - 5x + x - x + -0 x + x + 0 x - 9x + 56. (x - ( x - 5x + 6 x ( x - 5x + 6 - ( x - 5x + 6 x ( x + x(-5x + x(6 - ( x - (-5x - (6 x - 5 x + 6x - x + 5x - 8 x - 8 x + x - 8 57. ( x - ( x - x + 7 x ( x - x + 7 - ( x - x + 7 x ( x + x ( - x + x (7 - ( x - ( - x - (7 8 x 5 - x + x - x + x - 8 x 5 - x - x + 7 x - 58. (x - (x - (x - (x - (x(x + x(- - (x - (- (x - ( x - x - x + 6 (x - ( x - 8x + 6 (x - (x - ( x - 8x + 6 x ( x - 8x + 6 - ( x - 8x + 6 x ( x + x(-8x + x(6 - ( x - (-8x - (6 x - 8 x + 6x - x + x - 6 x - x + 8x - 6 59. (x - ( x + x + x ( x + x + - ( x + x + x ( x + x(x + x( - ( x - (x - ( x + x + x - x - x - x - x - 60. (x + 0 ( - x + 6 x x ( - x + 6 x + 0 ( - x + 6 x x( + x(-x + x ( 6 x + 0( + 0(-x + 0 ( 6 x 8x - x + x + 0-0x + 60 x x + 60 x - x - x + 0 6. ( - x ( - x( - x( - x (( + (-x - x( - x(-x ( - x ( - x - x + x ( - x ( - x + x ( - x ( - x ( - x + x ( - x + x - x ( - x + x - x + x -x( - x(-x -x ( x - x + x - x + x - x - x + x - x + 6a. A lw (x + (x x(x + (x x + x The area is represented by x + x. 76 Holt McDougal Algebra

b. A x + x (5 + (5 5 + 5 0 The area is 0 ft. 6. A s (x - 6 (x - 6(x - 6 x(x + x(-6-6(x - 6(-6 6 x - x - x + 6 6 x - 8x + 6 The area is represented by 6 x - 8x + 6. 6a. b. A lw (x + (x + x(x + x( + (x + ( x + x + x + x + 5x + The area is represented by x + 5x +. c. A x + 5x + ( + 5( + 6 + 0 + 0 The area is 0 ft. A Degree of A B Degree of B A B Degree of A B x x 5 5 6 x 7 7 65a. 5 x x + 0 x 5 + 5 x 5 b. x + x - x x - x + x - x c. x - x - x + x - 5 x + 6 x + x - d. m + n 66. A lw (x + (x x(x + (x 8 x + x The area is represented by 8 x + x. 67. A lw (x + (x + [(x + (](x + (6x + (x + 6x(x + 6x( + (x + ( x + 6x + 6x + x + x + The area is represented by x + x +. 68. A lw (x - 5(x - 5 x(x + x(-5-5(x - 5(-5 x - 5x - 5x + 5 x - 0x + 5 The area is represented by x - 0x + 5. 69a. A lw (x(x x The area is represented by x. b. A x (0 (00 800 The area is 800 m. 70. (.5 a ( a 6 (.5 ( a a 6 6 a 9 7. (x + 5(x - 6 x(x + x(-6 + 5(x + 5(-6 x - x + 5x - 0 x - 7x - 0 7. (g - (g + 5 g(g + g(5 - (g - (5 g + 5g - g - 5 g + g - 5 7. (x - y(x - y x(x + x(-y - y(x - y(-y 8 x - xy - xy + 6 y 8 x - 6xy + 6 y 7. (x + (x - x(x + x(- + (x + (- x - x + x - 9 x - 9 75. (.5x - (x +.5x(x +.5x( - (x - ( 6 x + x - x - 6 6 x - 9x - 6 76. (x - 0(x + x(x + x( - 0(x - 0( x + x - 0x - 0 x - 6x - 0 77. x (x + x (x + x ( x + x 78. (x + ( x + x x ( x + x(x + ( x + (x x + x + x + x x + x + x 77 Holt McDougal Algebra

79. (x - ( x + x - 6 x ( x + x - 6 - ( x + x - 6 x ( x + x(x + x(-6 - ( x - (x - (-6 x + x - 6x - 8 x - x + x - 7 x - 0x + 80. (a + b (a - b (a + b(a - b(a - b (a(a + a(-b + b(a + b(-b (a - b ( a - ab + ab - b (a - b ( a - b (a - b a (a + a (-b - b (a - b (-b a - a b - a b + b 8. (p - q (p - q(p - q(p - q (p(p + p(-q - q(p - q(-q ( p - q 8a. ( p - 6pq - 6pq + 9 q (p - q ( p - pq + 9 q (p - q (p - q ( p - pq + 9 q p ( p - pq + 9 q - q ( p - pq + 9 q p ( p + p(-pq + p (9 q - q ( p - q(-pq - q (9 q 8 p - p q + 8p q - p q + 6p q - 7 q 8 p - 6 p q + 5p q - 7 q b. The length is 5 + x + x x + 5. The width is 0 + x + x x + 0. c. A lw (x + 5(x + 0 x(x + x(0 + 5(x + 5(0 x + 0x + 50x + 50 x + 70x + 50 8. Possible answer: Each letter in FOIL represents a pair of terms in a certain position within the factors. The letters must account for every pairing of terms while describing first, outside, inside, and last positions. This is only possible with two binomials. 8. A lwh (x + 5(x(x + (x(x + 5(x (x + ( x + 5x (x + x (x + x ( + 5x(x + 5x( x + x + 5 x + 0x x + 7 x + 0x The area is represented by x + 7 x + 0x. 85. Yes; x 0 86. Let x represent the width of the rectangle. A lw (x + (x x(x + (x x + x Since (.5 +.5 0.5 +.5 5, the width of the rectangle is about.5 ft. TEST PREP 87. C (a + (a - 6 a(a + a(-6 + (a + (-6 a - 6a + a - 6 a - 5a - 6 88. H a ( a - a ( a + a(- a - a 89. D x y z x yz ( ( x x ( y y (z z x 5 y z This has degree 5 + + 0. CHALLENGE AND EXTEND 90. 6 x - ( x - x + 6 x - ( x - (-x - ( 6 x - 6 x + x - 8 x - 8 9. x - x(x + x - x(x - x( x - x - 6x - x - 6x 9. x(x - + x(x + x(x + x(- + x(x + x( x - x + x + x 7 x + x 9a. A lw (x + (x - x(x + x(- + (x + (- x - x + x - x - The area is represented by x -. b. A lw (x + 5(x + - (x + (x - x(x + x( + 5(x + 5( - ( x - x + x + 5x + 5 - x + 8x + 6 78 Holt McDougal Algebra

9. A s (8 + x (8 + x(8 + x 8(8 + 8(x + x(8 + x(x 6 + 6x + 6x + x x + x + 6 P s ( x + 8 ( x + (8 x + 9 A P x + x + 6 x + 9 - x - x x + 6 9-6 _ -6 x 8 _ x _ 8 x 95. x(x + (x + (x(x + x( (x + ( x + x (x + x (x + x ( + x(x + x( x + x + x + x x + x + x 96. x m ( x n + x n - x 5 + x x m ( x n + x m ( x n - x 5 + x x m + n + x m + n - x 5 + x Therefore, it must be true that: m + n 5 m + n 5 m + n - m + n 5 Therefore, the system is consistent and dependent, so there is an infinite number of solutions. One is m ; n. 97. x a (5 x a - + x a + 0 x + x 8 x a ( 5 x a - + x a ( x a + 0 x + x 8 0 x a - + x a + 0 x + x 8 Therefore, it must be true that: a - and a + 8 + + - - a 6 and a 6 a 6 a 6 a SPIRAL REVIEW 98. Let x represent the height of the flagpole. x.5 8.5.5x 70 _.5x.5 70.5 x 0 The flagpole is 0 m tall. 99. d (x - x + (y - y d ( - + (6 - d + d d.6 00. d (x - x + (y - y d (0 - (- + (8 - d + d 7 d. 0. d (x - x + (y - y d (-6 - (- + (- - 7 d ( - + (-9 d 90 d 9.9 0. Graph the boundary line y x -. Use a solid line for. The inequality is, so shade below the line. 0. x - y < 0 -x _ -x -y < -x + 0 _ -y > -x + 0 - - y > x - 5 Graph the boundary line y x - 5. Use a dashed line for >. The inequality is >, so shade above the line. 79 Holt McDougal Algebra

0. -y -x + -(-y -(-x + y x - Graph the boundary line y x -. Use a solid line for. The inequality is, so shade below the line. 7-9 SPECIAL PRODUCTS OF BINOMIALS, PAGES 5 57 CHECK IT OUT! a. (a + b a + ab + b (x + 6 (x + (x(6 + (6 x + x + 6 b. (a + b a + ab + b (5a + b (5a + (5a(b + (b 5 a + 0ab + b c. (a + b a + ab + b ( + c ( + ( ( c + ( c + c + c 6 a. (a - b a - ab + b (x - 7 (x - (x(7 + (7 x - x + 9 b. (a - b a - ab + b (b - c (b - (b(c + (c 9 b - bc + c c. (a - b a - ab + b ( a - ( a - ( a ( + ( a - 8 a + 6 a. (a + b(a - b a - b (x + 8(x - 8 (x - (8 x - 6 b. (a + b(a - b a - b ( + y ( - y ( - ( y 9 - y c. (a + b(a - b a - b (9 + r(9 - r (9 - (r 8 - r. Area of : (5 + x(5 - x (5 - (x 5 - x Area of : x Total area area of + area of ( 5 - x + x 5 + (- x + x 5 The area of the pool is 5. THINK AND DISCUSS. (a + b(a - b a - ab + ab - b a - b. product. EXERCISES GUIDED PRACTICE. Possible answer: a trinomial that is the result of squaring a binomial.. (a + b a + ab + b (x + 7 (x + (x(7 + (7 x + x + 9. (a + b a + ab + b ( + x ( + ((x + (x + x + x. (a + b a + ab + b (x + (x + (x( + ( x + x + 5. (a + b a + ab + b (x + 6 (x + (x(6 + (6 x + x + 6 6. (a + b a + ab + b (5x + 9 (5x + (5x(9 + (9 5 x + 90x + 8 7. (a + b a + ab + b (a + 7b (a + (a(7b + (7b a + 8ab + 9 b 8. (a - b a - ab + b (x - 6 (x - (x(6 + (6 x - x + 6 9. (a - b a - ab + b (x - (x - (x( + ( x - x + 0. (a - b a - ab + b (x - (x - (x( + ( x - x +. (a - b a - ab + b (8 - x (8 - (8(x + (x 6-6x + x. (a - b a - ab + b (6p - q (6p - (6p(q + (q 6 p - pq + q 80 Holt McDougal Algebra

. (a - b a - ab + b (7a - b (7a - (7a(b + (b 9 a - 8ab + b. (a + b(a - b a - b (x + 5(x - 5 (x - (5 x - 5 5. (a + b(a - b a - b (x + 6(x - 6 (x - (6 x - 6 6. (a + b(a - b a - b (5x + (5x - (5x - ( 5 x - 7. (a + b(a - b a - b ( x + ( x - ( x - ( x - 9 8. (a - b(a + b a - b ( 9 - x (9 + x (9 - ( x 8 - x 6 9. (a - b(a + b a - b (x - 5y(x + 5y (x - (5y x - 5 y 0. Area of big : (x + (x + (x( + ( x + 6x + 9 Area of small : (x + (x + (x( + ( x + x + Total area area of big + area of small ( x + 6x + 9 + ( x + x + ( x + x + (6x + x + (9 + x + 8x + 0 The area of the figure is x + 8x + 0. PRACTICE AND PROBLEM SOLVING. (a + b a + ab + b (x + (x + (x( + ( x + 6x + 9. (a + b a + ab + b ( + z ( + ((z + (z 6 + 8z + z. (a + b a + ab + b ( x + y ( x + ( x ( y + ( y x + x y + y. (a + b a + ab + b (p + q (p + (p ( q + ( q p + p q + q 6 5. (a + b a + ab + b ( + x ( + ((x + (x + x + 9 x 6. (a + b a + ab + b ( r + 5t ( r + ( r (5t + (5t r + 0 r t + 5 t 7. (a - b a - ab + b ( s - 7 ( s - ( s (7 + (7 s - s + 9 8. (a - b a - ab + b ( c - d (c - (c ( d + ( d c - c d + d 6 9. (a - b a - ab + b (a - 8 (a - (a(8 + (8 a - 6a + 6 0. (a - b a - ab + b (5 - w (5 - (5(w + (w 5-0w + w. (a - b a - ab + b (x - (x - (x( + ( 9 x - x + 6. (a - b a - ab + b ( - x ( - ( ( x + ( x - x + x. (a - b(a + b a - b (a - 0(a + 0 (a - (0 a - 00. (a + b(a - b a - b (y + (y - (y - ( y - 6 5. (a + b(a - b a - b (7x + (7x - (7x - ( 9 x - 9 6. (a - b(a + b a - b ( x - ( x + ( x - ( x - 7. (a + b(a - b a - b (5 a + 9 ( 5 a - 9 ( 5 a - (9 5 a - 8 8. (a + b(a - b a - b ( x + y ( x - y ( x - ( y 9. A π r π (x + x 6 - y π ( (x + (x( + ( π ( x + 8x + 6 π ( x + π(8x + π(6 π x + 8πx + 6π The area of the puzzle is π x + 8πx + 6π. 8 Holt McDougal Algebra