1. 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

2. Objective
Multiply polynomials.

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

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

5. ( ) ( ) Multiply. æ 1 ö (2r2t)(5t3) x y 12 x z y z ç ÷ è 3 ø 4 x y z7 5 4 x y z
10r2t4

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

7. ( ) 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

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

9. Multiply.
(s + 4)(s – 2)

10. 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

11. Multiply.
(x – 4)2

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

13. Multiply.
(x – 3)2

14. Multiply.
(2a – b2)(a + 4b2)

15. 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)

17. Multiply.
(x – 5)(x2 + 4x – 6)

18. Multiply.
(2x – 5)(–4x2 – 10x + 3)

19. Multiply.
(x + 3)3

20. Multiply.
(3x + 1)(x3 – 4x2 – 7)

21. Multiply.
(x + 3)(x2 – 4x + 6)

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

23. 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 /27-69 Odd, 75-84, 87-89,  Even