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5.5 and 5.65.5 and 5.6Multiply Multiply

PolynomialsPolynomials

5.5 and 5.65.5 and 5.6Multiply Multiply

PolynomialsPolynomials

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Examples: 1. Multiply: (2x + 2)2 .

(a + b)2 = (a + b)(a + b)

= a2 + 2ab + b2

= (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

= a2 + ab + ab + b2

To square a binomial, use this pattern:

square of the first term

twice the product of the two terms square of the last term

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Examples: 1. Multiply: (2x – 2)2 .

(a - b)2 = (a - b)(a - b)

= a2 - 2ab + b2

= (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

= a2 - ab - ab + b2

To square a binomial, use this pattern:

square of the first term

twice the product of the two terms square of the last term

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Examples: 1. (3x + 2)(3x – 2)

(a + b)(a – b)

= a2 – b2

= (3x)2 – (2)2

= 9x2 – 4

2. (x + 1)(x – 1)= (x)2 – (1)2

= x2 – 1

To multiply the sum and difference of two terms,

use this pattern:

= a2 – ab + ab – b2

square of the first termsquare of the second term

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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 ) = x2 – 6x + 5x – 30

= x2 – x – 30

The area is (x2 – x – 30) ft2.