holt algebra 2 6-2 multiplying polynomials multiply polynomials. use binomial expansion to expand...

Holt Algebra 2

6-2 Multiplying Polynomials

Multiply polynomials.

Use binomial expansion to expand binomial expressions that are raised to positive integer powers.

Objectives

To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

Holt Algebra 2

6-2 Multiplying Polynomials

Find each product.

Example 1: Multiplying a Monomial and a Polynomial

A. 4y2(y2 + 3)

B. fg(f4 + 2f3g – 3f2g2 + fg3)

4y2 y2 + 4y2 3

4y2(y2 + 3)

4y4 + 12y2

fg(f4 + 2f3g – 3f2g2 + fg3)

fg f4 + fg 2f3g – fg 3f2g2 + fg fg3

f5g + 2f4g2 – 3f3g3 + f2g4

Holt Algebra 2

6-2 Multiplying Polynomials

Check It Out! Example 1

Find each product.

a. 3cd2(4c2d – 6cd + 14cd2)

b. x2y(6y3 + y2 – 28y + 30)

Holt Algebra 2

6-2 Multiplying Polynomials

To 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.

Holt Algebra 2

6-2 Multiplying Polynomials

Find the product.

Example 2A: Multiplying Polynomials

(a – 3)(2 – 5a + a2)

a(a2) + a(–5a) + a(2) – 3(a2) – 3(–5a) –3(2)

Method 1 Multiply horizontally.

a3 – 5a2 + 2a – 3a2 + 15a – 6

a3 – 8a2 + 17a – 6

(a – 3)(a2 – 5a + 2)

Holt Algebra 2

6-2 Multiplying Polynomials

(a – 3)(2 – 5a + a2)

Find the product.

Example 2A: Multiplying Polynomials

Method 2 Multiply vertically.

a2 – 5a + 2 a – 3

– 3a2 + 15a – 6a3 – 5a2 + 2a

a3 – 8a2 + 17a – 6

Holt Algebra 2

6-2 Multiplying Polynomials

Check It Out! Example 2a

Find the product.

(3b – 2c)(3b2 – bc – 2c2)

Multiply horizontally.

Holt Algebra 2

6-2 Multiplying Polynomials

(x2 – 4x + 1)(x2 + 5x – 2)

Find the product.Check It Out! Example 2b

Multiply vertically

Holt Algebra 2

6-2 Multiplying PolynomialsFind the product. (a + 2b)3

Holt Algebra 2

6-2 Multiplying PolynomialsFind the product. (x + 4)4

Holt Algebra 2

6-2 Multiplying Polynomials

Find the product. (2x – 1)3

Holt Algebra 2

6-2 Multiplying Polynomials

Lesson Quiz

2. (2a3 – a + 3)(a2 + 3a – 5)

5jk2 – 10j2k1. 5jk(k – 2j)

2a5 + 6a4 – 11a3 + 14a – 15

Find each product.

3. (3a – b)3

27a3 – 27a2b + 9ab2 – b3