1. Multiplication: Special Cases
Section 5.5
Multiplication: Special Cases

2. Multiplying Binomials
Multiplying Binomials: A Sum and a Difference
(a + b)(a  b) = a2 – b2

3. Example Multiply. (2x + 4)(2x  4) (2x + 4)(2x  4) = (2x)2 – (4)23

4. Examples Multiply. a. (5a + 3)(5a  3) = (5a)2  32 b. = 25a2  9
(8c + 2d)(8c  2d)
= (8c)2  (2d)2
= 64c2  4d2 4

5. Multiplying Binomials
A Binomial Squared
(a + b)2 = a2 + 2ab + b2
(a  b)2 = a2 – 2ab + b2

6. Example Multiply. (x + 6)2 (x + 6)2 = (x)2 + 2(x)(6) + (6)2

7. Example Multiply. a. (12a  3)2 = (12a)2  2(12a)(3) + (3)2
b. (x + y)2
= (12a)2  2(12a)(3) + (3)2
= 144a2  72a + 9
= x2 + 2xy + y2 7

8. Example
To multiply any two polynomials, vertical multiplication may be used.
Multiply. (w – 1)(2w2 + 7w + 3)
Write vertically, lining up the terms.
2w2 + 7w + 3
w – 1
Keep the terms lined up.
– 2w2 – 7w – 3
Multiply – 1(2w2 + 7w + 3).
2w3 + 7w2 + 3w
Multiply w(2w2 + 7w + 3).
2w3 + 5w2 – 4w – 3
Add the terms in each column. 8

9. Example
To multiply any two polynomials, the distributive property may also be used.
Multiply. (w – 1)(2w2 + 7w + 3)
Multiply the first term in the first polynomial by every term in the second polynomial…
(w – 1)(2w2 + 7w + 3)
= w(2w2) + w(7w) + w(3) +
(–1)2w2 + (–1)7w + (–1)3
… and multiply the second term in the first polynomial by every term in the second polynomial.
= 2w3 + 7w2 + 3w + (–2w2) + (–7w) + (–3)
= 2w3 + 5w2 – 4w – 3 9