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1 5.5 and 5.6 Multiply Polynomials

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2 Square of a Binomial Examples: 1. Multiply: (2x + 2) 2. (a + b) 2 = (a + b)(a + b) = a 2 + 2ab + b 2 = (2x) 2 + 2(2x)( 2) + (2) 2 = 4x 2 + 8x Multiply: (x + 3y) 2. = (x) 2 + 2(x)(3y) + (3y) 2 = x 2 + 6xy + 9y 2 = a 2 + ab + ab + b 2 To square a binomial, use this pattern: square of the first term twice the product of the two termssquare of the last term

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3 Square of a Binomial Examples: 1. Multiply: (2x – 2) 2. (a - b) 2 = (a - b)(a - b) = a 2 - 2ab + b 2 = (2x) 2 + 2(2x)(– 2) + (– 2) 2 = 4x 2 – 8x Multiply: (x - 4y) 2. = (x) 2 + 2(x)(4y) + (4y) 2 = x 2 + 8xy + 16y 2 = a 2 - ab - ab + b 2 To square a binomial, use this pattern: square of the first term twice the product of the two termssquare of the last term

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4 Special Products Examples: 1. (3x + 2)(3x – 2) (a + b)(a – b) = a 2 – b 2 = (3x) 2 – (2) 2 = 9x 2 – 4 2. (x + 1)(x – 1) = (x) 2 – (1) 2 = x 2 – 1 To multiply the sum and difference of two terms, use this pattern: = a 2 – ab + ab – b 2 square of the first term square of the second term

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5 Example: Word Problem Example: The length of a rectangle is (x + 5) ft. The width is (x – 6) ft. Find the area of the rectangle in terms of the variable x. A = L · W = Area x – 6 x + 5 L = (x + 5) ft W = (x – 6) ft A = (x + 5)(x – 6 ) = x 2 – 6x + 5x – 30 = x 2 – x – 30 The area is (x 2 – x – 30) ft 2.

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