Algebra 2

1
Algebra 2 Section 3.2 Special Products
When multiplying polynomials, there are patterns
(shortcuts) to follow in order to save time and
work.
Product of sum and difference of two terms
1. (a b)(a b) a2 b2
Square of a binomial 2. (a b)2 a2
2ab b2 3. (a b)2 a2 2ab b2
Two special products 4. (a b)(a2 ab
b2) a3 b3 5. (a b)(a2 ab b2) a3 b3

2
Just decide which of the patterns the
multiplication matches up with and follow it.
1. (a b)(a b) a2 b2 2. (a b)2
a2 2ab b2 3. (a b)2 a2 2ab b2 4.
(a b)(a2 ab b2) a3 b3 5. (a b)(a2
ab b2) a3 b3
1. (a b)(a b) a2 b2
(n 12)(n 12)
n2 144
4. (a b)(a2 ab b2) a3 b3
If a n and b 12 then a2 n2 b2 122
144
(4x 5)(16x2 20x 25)
64x3 125
If a 4x and b 5 then a3 (4x)3 64x3
b3 53 125
2. (a b)2 a2 2ab b2
4x2 12x 9
(2x 3)2
If a 2x and b 3 then a2 (2x)2 4x2
2ab 2(2x)(3) 12x b2 32 9
3
1. (a b)(a b) a2 b2 2. (a b)2
a2 2ab b2 3. (a b)2 a2 2ab b2 4.
(a b)(a2 ab b2) a3 b3 5. (a b)(a2
ab b2) a3 b3
(a b)2 a2 2ab b2
(1 6n)2
1 12n 36n2
a 1 and b 6n then a2 12 1 2ab
2(1)(6n) 12n b2 (6n)2 36n2
(a b)(a b) a2 b2
(25 3y)(25 3y)
625 9y2
If a 25 and b 3y then a2 252 625
b2 (3y)2 9y2
(a b)(a2 ab b2) a3 b3
(3y 1)(9y2 3y 1)
27y3 - 1
If a 3y and b 1 then a3 (3y)3 27y3
b3 13 1