1. 5.5 and 5.6 Multiply Polynomials

2. 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

3. 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

4. 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

5. 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