5.5 and 5.6 Multiply Polynomials

To square a binomial, use this pattern: (a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2 = a2 + 2ab + b2 square of the first term twice the product of the two terms square of the last term Examples: 1. Multiply: (2x + 2)2 . = (2x)2 + 2(2x)( 2) + (2)2 = 4x2 + 8x + 4 2. Multiply: (x + 3y)2 . = (x)2 + 2(x)(3y) + (3y)2 = x2 + 6xy + 9y2 Square of a Binomial

To square a binomial, use this pattern: (a - b)2 = (a - b)(a - b) = a2 - ab - ab + b2 = a2 - 2ab + b2 square of the first term twice the product of the two terms square of the last term Examples: 1. Multiply: (2x – 2)2 . = (2x)2 + 2(2x)(– 2) + (– 2)2 = 4x2 – 8x + 4 2. Multiply: (x - 4y)2 . = (x)2 + 2(x)(4y) + (4y)2 = x2 + 8xy + 16y2 Square of a Binomial

To multiply the sum and difference of two terms, use this pattern: (a + b)(a – b) = a2 – ab + ab – b2 = a2 – b2 square of the second term square of the first term Examples: 1. (3x + 2)(3x – 2) 2. (x + 1)(x – 1) = (3x)2 – (2)2 = (x)2 – (1)2 = 9x2 – 4 = x2 – 1 Special Products

Example: The length of a rectangle is (x + 5) ft 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. x – 6 x + 5 A = L · W = Area L = (x + 5) ft W = (x – 6) ft A = (x + 5)(x – 6 ) = x2 – 6x + 5x – 30 = x2 – x – 30 The area is (x2 – x – 30) ft2. Example: Word Problem