Name Class Date. Expanding Algebraic Expressions. 4. Use the Distributive Property to expand the expression 7(9x 2).

Transcription

1 Name Class Date Practice 7-1 Expanding Algebraic Expressions 7-1 Expanding Algebraic Expressions 1. Find a sum equivalent to the product 6(y + x). 2. Find a difference equivalent to the product 11(x y). 3. Expand 3(n + 7). 4. Use the Distributive Property to expand the expression 7(9x 2). 5. An architect plans to build an extension to your rectangular Let x represent the increase, in meters, of your kitchen s length. The expression 5(x + 8) represents the area of your kitchen, where 5 is the width, in meters, and (x + 8) represents the extended length, in meters, of your a) Which expression is equivalent to 5(x + 8)? A. 6x + 13 C. 5x + 8 B. 5x + 40 D. x + 40 b) What does each term of the new expression represent? A. x represents the area, in square meters, of the new portion of your 40 represents the area, in square meters, of your existing B. 6x represents the area, in square meters, of the new portion of your 13 represents the area, in square meters, of your existing C. 5x represents the area, in square meters, of the new portion of your 8 represents the area, in square meters, of your existing D. 5x represents the area, in square meters, of the new portion of your 40 represents the area, in square meters, of your existing 6. A local bookstore is advertising $3 off the price of each book. You decide to buy 6 books. Let p represent the price of each book. Use the expression 6(p 3). a) What do the factors of 6(p 3) represent? A. 6 represents the number of books purchased and p 3 represents the original price of each book. B. p 3 represents the number of books purchased and 6 represents the original price of each book. C. p 3 represents the number of books purchased and 6 represents the discounted price of each book. D. 6 represents the number of books purchased and p 3 represents the discounted price of each book. 1

2 b) Which expression shows the correct expansion? What do the terms of the new expression represent? A. p 18; p represents the cost of the books before the discount and 18 represents the amount of the discount. B. 6p 18; 6p represents the cost of the books before the discount and 18 represents the original price. C. 6p 18; 6p represents the cost of the books before the discount and 18 represents the amount of the discount. D. p 18; p represents the cost of the books before the discount and 18 represents the original price. 7. Reasoning The expressions 2(30x 24), 3(20x 16), and 4(15x 12) all have the same expansion. a) Which expression is equivalent to 2(30x 24), 3(20x 16), and 4(15x 12)? A. 80x 36 C. 60x 48 B. 90x 48 D. 60x 36 b) Explain why the three expressions have the same expansion. 8. Geometry The perimeter of a square can be found using the formula P = 4s where s is the side length of the square. If you were to increase the length s by 9, the expression for the perimeter would become 4(s + 9). Which expression represents the perimeter of the larger square? A. 4s + 36 C. s + 36 B. 5s + 13 D. 4s a) Open-Ended Expand the expression 1 ( 4 t - 10 ). 2 b) Describe a situation in which you would want to write and then expand an algebraic expression. 10. a) Writing Use the Distributive Property to expand 3(4x + 2). b) How are the expressions the same? Explain. c) How are the expressions different? Explain. 11. Error Analysis A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the garden s original length. The expression 9(x + 7) represents the area of the garden, where 9 is the width, in feet, and (x + 7) represents the extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was 16 square feet. a) Which answer represents the correct expansion and the correct area of the extension? A. 10x + 16; the area of the extension is 10x square feet. B. 9x + 63; the area of the extension is 9x square feet. C. 9x + 7; the area of the extension is 7 square feet. D. 9x + 63; the area of the extension is 63 square feet. 2

3 b) Which answer describes an error the gardener might have made? A. When using the Distributive Property to expand the expression, the gardener multiplied each term in the parentheses by 9. The gardener should have only multiplied the first term. B. When using the Distributive Property to expand the expression, the gardener added 9 to each term in the parentheses. The gardener should have multiplied. C. The gardener distributed the 9 to each term correctly but chose the incorrect term of the sum as the area. D. When using the Distributive Property to expand the expression, the gardener multiplied each term in the parentheses by 9. The gardener should have added. 12. Multiple Representation a) Which expression is equivalent to 8(6x 4)? A. 2x 4 C. 48x 4 B. 6x 32 D. 48x 32 b) Draw an algebra tile model for each expression. Then demonstrate how both expressions are equal. 13. Which expression is equivalent to 4(7(7x 3y) 6)? A. 49x 12y 24 C. 196x 3y 6 B. 49x 84y 24 D. 196x 84y Challenge The bakery manager at the grocery store decides to have an 18% off sale on all bread. You decide to purchase 5 loaves of bread. Let b be the original price of a loaf of bread. a) Which expression represents the correct expansion of the expression 5(b 0.18b)? A. 5b b C. 5b 0.90b B. 5b 0.90 D. 5b b) What do the terms of the expansion represent? A. 5b represents the cost of 5 loaves of bread at the original price is subtracted from 5b to find the sale price. B. 5b represents the cost of 5 loaves of bread at the original price. 0.90b is added to 5b to find the sale price. C. 5b represents the cost of 5 loaves of bread at the original price is added to 5b to find the sale price. D. 5b represents the cost of 5 loaves of bread at the original price. 0.90b is subtracted from 5b to find the sale price. 3

4 15. Challenge The length of a square garden has been extended by 10 feet. Use the fact that the area of a rectangle is L# W and L = W + 10 to write an expression for the area of the rectangular garden as a product of two factors. a) Which expression represents the area of the rectangular garden? What does each factor represent? A. L(W + 10); L is the length and (W + 10) is the width. B. L(W 10); L is the length and (W 10) is the width. C. W(W 10); W is the width and (W 10) is the length. D. W(W + 10); W is the width and (W + 10) is the length. b) Which expression represents the correct expansion? What does each term of the expansion represent? A. W W; W 2 represents the area of the once square garden and 10W represents the area of the extension. B. LW + 10W; LW represents the area of the once square garden and 10W represents the area of the extension. C. LW 10W; LW represents the area of the once square garden and 10W represents the area of the extension. D. W 2 10W; W 2 represents the area of the once square garden and 10W represents the area of the extension. 4

5 ANSWER KEY : Expanding Algebraic Expressions 1. 6y + 6x 2. 11x 11y 3. 3n x a) B b) D 6. a) D b) C 7. a) C 8. A 9. a) 2t a) 12x + 6 c) Answers will vary 11. a) D b) B 12. a) D 13. D 14. a) C b) D 15. a) D b) A 5 Answer Key G