First row Multiply first row by y Multiply first row by 2x Add the columns 4 2

First row multiply first row by y multiply first row

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First row Multiply first row by -y Multiply first row by 2x Add the columns ) 4 2 y)(4x - (2x Multiply 2 2 y xy 3 2 3 2 2 3 3 2 2 2 2 4 10 8 8 4 8 4 2 4 2 4 2 4 y xy x xy y x x y xy y x y x y xy x
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Multiply and simplify. -6t + 15 8x 2 + 13x – 6 4z 3 – 15z 2 + 13z – 3 5.2 Multiplication of Polynomials ) 1 3 )( 3 4 ( ) 2 )( 3 8 ( ) 5 2 ( 3 2 z z z x x t
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Real – World Connection: Business application 5.2 Multiplication of Polynomials Let the demand, D, or number of games sold in thousands, be given by , where p ≥ 16 is the price of the games in dollars. a) Find the demand where p = $30 and when p = $60. b) Write an expression for the revenue, R. Multiply the expression. c) Find the revenue when p = $40. p D 8 1 40 $1400,000 or 1400 200 1600 ) 40 ( 8 1 ) 40 ( 40 $40 p when Revenue c) 8 1 40 ) 8 1 40 ( mand) (price)(de Revenue b) games 500 , 32 ) 60 ( 8 1 40 $60, p when games 250 , 36 ) 30 ( 8 1 40 $30, p when a) 2 2 p p p p D D
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Use the formula (a + b) 2 = a 2 + 2ab + b 2 (2x + 1) 2 = (2x + 1)(2x + 1) where a = 2x and b = 1 , then (2x +1) 2 = (2x) 2 + 2(2x)(1) + 1 2 = 4x 2 + 4x + 1 Square of a Binomial – Square of a Sum 5.2 Multiplication of Polynomials
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Square of a Binomial – Square of a Difference 5.2 Multiplication of Polynomials Use the formula (a - b) 2 = a 2 - 2ab + b 2 (4m - 5) 2 = (4m - 5)(4m - 5) where a = 4m and b = 5 , then (4m - 5) 2 = (4m) 2 - 2(4m)(5) + 5 2 = 16m 2 40m + 25
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Product of a Sum and Difference 5.2 Multiplication of Polynomials Use the formula (a + b)(a - b) = a 2 - b 2 (2z + 5k 4 )(2z – 5k 4 ) where a = 2z and b = 5k 4 , then (2z + 5k 4 )(2z – 5k 4 ) = (2z) 2 – (5k 4 ) 2 = 4z 2 – 25k 8
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Product of a Sum and Difference 5.2 Multiplication of Polynomials Use the formula (a + b)(a - b) = a 2 - b 2 3rt(r – 2t)(r + 2t) where a = r and b = 2t , then 3rt(r – 2t)(r + 2t) = 3rt[ r 2 – (2t) 2 ] = 3rt(r 2 – 4t 2 ) = 3r 3 t – 12rt 3
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5.1 Polynomial Functions Multiplying polynomial functions: Evaluate f(3) and g(3) and multiply the results. 4 ) ( Let 3 2 ) ( Let 2 2 x x g x x x f ). )( ( and ) 3 )( ( Find x fg fg 117 13 9 ) 3 )( ( 13 4 3 ) 3 ( 9 9 18 ) 3 ( 3 ) 3 ( 2 ) 3 ( ) 3 )( ( 2 2 fg g f fg x x x x x x x x x x x x fg x x g x x x f x fg 12 8 3 2 12 3 8 2 ) 4 )( 3 2 ( ) )( ( 4 ) ( 3 2 ) ( ) )( ( 2 3 4 3 2 4 2 2 2 2
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5.5 Special Types of Factoring 5.4 Factoring Trinomials 5.3 Factoring Polynomials 5. 2 Multiplication of Polynomials 5.1 Polynomial Functions 5.7 Factoring Equations Chapter 5 – Polynomial Expressions and Functions
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Find the GCF for the following monomials using prime factorization. Each monomial has 2, 3, x, y, y in common. Multiply the common factors to get the GCF of 6xy 2 . 5.3 Factoring Polynomials Finding the Greatest Common Factor (GCF) y y x xy y y x x x y x y y y x x y x 3 3 2 18 3 2 2 2 24 3 3 2 2 36 2 2 3 3 2
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When factoring an expression, find the GCF for each term or monomial and put the remaining expression in parenthesis.
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