Title: Multiply polynomials.
1Objectives
Multiply polynomials. Use binomial expansion to
expand binomial expressions that are raised to
positive integer powers.
To multiply a polynomial by a monomial, use the
Distributive Property and the Properties of
Exponents.
2Example 1 Multiplying a Monomial and a Polynomial
Find each product.
A. 4y2(y2 3)
4y2(y2 3)
4y2 ? y2 4y2 ? 3
4y4 12y2
B. fg(f4 2f3g 3f2g2 fg3)
fg(f4 2f3g 3f2g2 fg3)
fg ? f4 fg ? 2f3g fg ? 3f2g2 fg ? fg3
f5g 2f4g2 3f3g3 f2g4
3Check It Out! Example 1
Find each product.
a. 3cd2(4c2d 6cd 14cd2)
b. x2y(6y3 y2 28y 30)
4To multiply any two polynomials, use the
Distributive Property and multiply each term in
the second polynomial by each term in the first.
Keep in mind that if one polynomial has m terms
and the other has n terms, then the product has
mn terms before it is simplified.
5Example 2A Multiplying Polynomials
Find the product.
(a 3)(2 5a a2)
Method 1 Multiply horizontally.
(a 3)(a2 5a 2)
a(a2) a(5a) a(2) 3(a2) 3(5a) 3(2)
a3 5a2 2a 3a2 15a 6
a3 8a2 17a 6
6Example 2A Multiplying Polynomials
Find the product.
(a 3)(2 5a a2)
Method 2 Multiply vertically.
3a2 15a 6
a3 5a2 2a
a3 8a2 17a 6
7Check It Out! Example 2a
Find the product.
Multiply horizontally.
(3b 2c)(3b2 bc 2c2)
8Check It Out! Example 2b
Find the product.
Multiply vertically
(x2 4x 1)(x2 5x 2)
9Find the product.
(a 2b)3
10Find the product.
(x 4)4
11Find the product.
(2x 1)3
12Lesson Quiz
Find each product.
1. 5jk(k 2j)
5jk2 10j2k
2. (2a3 a 3)(a2 3a 5)
2a5 6a4 11a3 14a 15
3. (3a b)3
27a3 27a2b 9ab2 b3