Warm Up Evaluate. 1. 32 3. 102 Simplify. 4. 23  24 6. (53)2 9 2. 24 16 100 27 5. y5  y4 y9 56 7. (x2)4 x8 8. –4(x – 7) –4x + 28

Objective Multiply polynomials.

To multiply polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.

Multiply. A. (6y3)(3y5) =18y8 B. (3mn2) (9m2n) =27m3n3

( ) ( ) Multiply. æ 1 ö (2r2t)(5t3) x y 12 x z y z ç ÷ è 3 ø 4 x y z 7 5 4 x y z 10r2t4

Multiply. 4(3x2 + 4x – 8) 12x2 + 16x – 32 (6pq)(2p – q) 12p2q – 6pq2

( ) Multiply. x y + 6 1 xy y x 8 3ab(5a2 + b) 15a3b + 3ab2 5r2s2(r – 3s) 2(4x2 + x + 3) 5r3s2 – 15r2s3 8x2 + 2x + 6

To multiply a binomial by a binomial, you can FOIL:

Multiply. (s + 4)(s – 2)

In the expression (x + 5)2, the base is (x + 5) In the expression (x + 5)2, the base is (x + 5). (x + 5)2 = (x + 5)(x + 5) Helpful Hint

Multiply. (x – 4)2

Multiply. (8m2 – n)(m2 – 3n) 8m4 – 24m2n – m2n + 3n2 8m4 – 25m2n + 3n2

Multiply. (x – 3)2

Multiply. (2a – b2)(a + 4b2)

To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6): (5x + 3)(2x2 + 10x – 6)

Multiply. (x – 5)(x2 + 4x – 6)

Multiply. (2x – 5)(–4x2 – 10x + 3)

Multiply. (x + 3)3

Multiply. (3x + 1)(x3 – 4x2 – 7)

Multiply. (x + 3)(x2 – 4x + 6)

The length of a rectangle is 4 meters shorter than its width. a. Write a polynomial that represents the area of the rectangle.

The length of a rectangle is 4 meters shorter than its width. b. Find the area of a rectangle when the width is 6 meters. HW Pages 497-499/27-69 Odd, 75-84, 87-89, 98-104 Even