1. Multiplying Polynomials
FOIL
FOIL
Section 7.8
Multiplying Polynomials
FOIL
FOIL

2. California
Standards
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.

3. Let’s Try Multiplying Monomials
A. (6y3)(3y5)
(6y3)(3y5)
Group factors with like bases together.
(6 3)(y3 y5) 
Multiply.
18y8
B. (3mn2) (9m2n)
Group factors with like bases together.
(3mn2)(9m2n)
(3 9)(m m2)(n2  n) 
Multiply.
27m3n3

4. Review of Distributive Property
3(x + 7)
= 3(x) + 3(7)
= 3x + 21
-2(-3 + 4y)
= -2(-3) + -2(4y)
= y

5. Multiplying Monomials and Polynomials
4(3x2 + 4x – 8)
4 (3x2 + 4x – 8)
Distribute 4.
(4)3x2 + (4)4x – (4)8
Multiply.
12x2 + 16x – 32

6. FOIL

7. FOIL
(2x + 1)(x – 5)

8. FOIL
(3x - 5)(2x + 7)

9. FOIL
(3x - 5)(2x + 7)

10. The box method
( )( ) 3x +5 4x +6
12x2
20x 30
18x
12x2 + 38x + 30

11. The box method
( )( ) 6x
+ 1 3x
- 2
18x2 3x -2
-12x
18x2 - 9x - 2

12. The box method
( )( ) 2x
- 3 4x
- 2
8x2
-12x 6
-4x
8x2 - 16x + 6

13. 20x3 - x2 - 22x + 8 The box method ( )( ) 5x - 4 4x2 +3x - 2 20x3 15x2
( )( ) 5x
- 4
4x2
+3x
- 2
20x3
15x2
-10x
-16x2
-12x 8
20x3 - x2 - 22x + 8

14. Challenge Multiply. (x – 5)(x2 + 4x – 6) Distribute x and –5.
Distribute x and −5 again.
x(x2 + 4x – 6) – 5(x2 + 4x – 6)
x(x2) + x(4x) + x(–6) – 5(x2) – 5(4x) – 5(–6)
Simplify.
x3 + 4x2 – 6x – 5x2 – 20x + 30
Combine like terms.
x3 – x2 – 26x + 30

15. Practice Problems Fill in the blank. (5a + 2)(6a – 1) = a2 + 7a – 2
(2x + 9)(x + 2) = 2x x + 18
(x + 3)2 = x 30 13 6x

16. Match D B A C (4x + 3)(3x + 2) (2x + 8)(6x + 2) (12x + 3)(x + 1)

17. Find Each Product 1. 4. 2. 5. 3. 6. 2x2 + 13x + 15 x2 + 7x + 10
(2y + 1)(3y + 4)
(2x + 3)(x + 5)
(10x + 10)(2x + 2)
(x + 7)2
2x2 + 13x + 15
x2 + 7x + 10 2. 5.
20x2 + 40x + 20
2x2 + 5x + 2 3. 6.
x2 + 14x + 49
6y2 + 11y + 4

18. Lesson Quiz Multiply. 1. (6s2t2)(3st) 2. 4xy2(x + y) 18s3t3
3. (x + 2)(x – 8)
4. (2x – 7)(x2 + 3x – 4)
5. 6mn(m2 + 10mn – 2)
6. (2x – 5y)(3x + y)
18s3t3
4x2y2 + 4xy3
x2 – 6x – 16
2x3 – x2 – 29x + 28
6m3n + 60m2n2 – 12mn
6x2 – 13xy – 5y2