MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1

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1 MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1

2 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication statement that is represented by the algebra tiles below. a) b) c) Miller High School Mathematics Page

3 . Using the algebra tiles, find the missing side. a) b) c) Miller High School Mathematics Page

4 Day : Lesson 7.1: Multiplying Monomials To multiply monomials algebraically, do the following: 1. Multiply the. Use the rule to multiply the variables. How? the exponents. Ex. 1: Multiply the monomials a) (4x)(y) b) ( x)(7x) x c) ( x y)( x y ) d) 15x e) (11a)(b) f) (-5x)(.) g) (-6a)(-4a) h) (4x)(0.5x) Miller High School Mathematics Page 4

5 Day : Lesson 7.1: Dividing Monomials To divide monomials algebraically, do the following: 1. Divide the. Use the rule to divide the variables. How? the exponents. Ex. 1: Divide the monomials 4x a) b) x 6x y4 xy c) x y x d) 1 x x e) 0x² (-x) f) -ac -8ac. g) 1xy y i) -14x² -x Miller High School Mathematics Page 5

6 Day 4 & 5: Lesson 7.: Multiplying Polynomials by Monomials 7.1 Quiz To multiply polynomials by monomials,. Use the property, which allows us to expand algebraic expressions. 4. How? We do this by the monomial by each term in the polynomial. ( a)( b c) ab bc Ex. 1: Use the distributive property to expand each expression: a) (x)(x+) b) (+c)(c) x d) 4x (x 1) c) ( )(x 6) e) 4 x (6x 1) f) (4.n)(n 7) g) (b)(-0.1a+8b-0.7c) h) (7v)(-7v-7x) Miller High School Mathematics Page 6

7 Area models can also be used to expand expressions. Ex :What polynomial multiplication statement is represented by the area model shown? Simplify.. Day 6 & 7: Lesson 7.: Dividing Polynomials by Monomials To divide a polynomial by a monomial, you can divide the numerical and apply the laws to the variables. You can also use algebra tiles to divide a polynomial by a binomial 4x 6x x 4x x 6x x 4x 6x x x x When using algebra tiles, the unknown side length of the rectangle is made up of x- tiles Example 1: Determine the polynomial division statement shown by the algebra tiles. Determine the quotient. a) b) Miller High School Mathematics Page 7

8 Example : Determine each quotient a) 15x 0 5x x b) 16m 0 4m mn c) 18k 9 9k k d) 1m 18mn 6m e) d dk d d f) 9c 1c 6 Complete the Show you know on page 7! Miller High School Mathematics Page 8

9 Lesson : Solving Word Problems Involving Multiplying and Dividing Polynomials Day 8: 7.1 Multiplying and Dividing Monomials Example 1: 1) What is an expression for the area of a rectangle with a width of w and a length of.w. ) The area of a triangle is given by the expression 0x. The base of the triangle is represented by 5x. What is the height of the triangle? ) Marko s rectangular lawn has an area of 6x m². The length of the lawn is 9 m. Marko wants to add a circular cement patio. What is the area of the largest circular patio that he could add? Show all calculations. 7. Multiplying Polynomials by Monomials Example : 1) What is an expression for the area of a rectangle with a width of w and a length of (w+1)? Miller High School Mathematics Page 9

10 ) The length of a cement pad on a playground is m longer than the width. The width is 5x m. a) Write an expression for the area of the cement pad. b) If x = m, what is the area of the cement pad? Day 9: 7. Dividing Polynomials by Monomials Example : 1) You are decorating the bulletin board in your classroom with pictures of your classmates. Each picture covers an area of 4x cm². The area of the board is 4x² + 16x cm². Write an expression to represent how many pictures are required to cover the board. ) A triangle has a base of (x + 10) cm and a height of 1x cm. Write an expression you can use to calculate the area of the triangle. Miller High School Mathematics Page 10

11 Math Links 9 Chapter 7 Review for Midterm Polynomials Polynomial an algebraic expression formed by adding or subtracting terms. a) Monomial 1 term (ex. x y z ) b) Binomial terms (ex. x y ) c) Trinomial terms (ex. x x 4) Like terms a term with the same variables raised to the same exponents. Unlike terms a term with different variables raised to different exponents. Variables a symbol used to represent a number Degree of a term The sum of the exponents of the variables Examples Degree 4x xy 1 + = 4 5a b c = 9 Degree of a polynomial The highest power of the variable in any one term Examples Degree x xy x y x y 6y x 8 Numerical coefficient the number that precedes a variable Constant term a number only term It is always a good habit to arrange in Order of descending powers. a) Largest power of x first b) largest power of x first Ex. x x 5x 7 4 Ex. 4xy x y x = 5 4 x x x 7 = x x y 4xy Miller High School Mathematics Page 11

12 Examples: Multiplying & Dividing Monomials by Monomials Multiply When multiply monomials, 1. multiply the coefficients. add the exponents 4 a) ( x )(4x) = b) ( x )(x ) c) ( 6ab c )( a b ) = d) 4x y ( x y )(6x ) Dividing When dividing monomials, 1. Divide the coefficients. Subtract the exponents 4x a) 5 16x b) 8x 10x y c) 5y d) 8 15a b c 5 10a b c 6a b e) 4 a b 4 1x y z f) 6 x yz Practice 1. a) Arrange in descending powers of x. b) Arrange in ascending powers of x. 4 5x y 14xy 1x 11y 5x yz xy 4 z x y 4 z. Simplify by multiplying or dividing. a) 6x7y b) x x 1 c) 1x y 7 z 6x yz 4 d) x yz xy z xyz Miller High School Mathematics Page 1

13 e) g) i) xy x y f) 6 rst rs h) 0a b c 7 15ab c 4 j) m 8 5x 6 y 8 15x 4 y 5 18x yz 5 4xy 4 z k) xy 5x y 18x 4 y l) 7x xy 7xy Solutions for Practice: a) 1x 5x y 14xy 11y b) xy z 5x yz x y z a) 4xy b) 4x c) 7x y z d) x y z e) 18x y f) 4m g) 1 t h) 1 x y i) k) 5y i) 7 x y 6 4a c j) xz 4y Miller High School Mathematics Page 1