Name
Date
Class
Reteach
LESSON
6-2
Multiplying Polynomials
Use the Distributive Property to multiply a monomial and a polynomial.
Think: k x y z kx ky kz
Multiply: 2ab 2 3a 2b 4ab 2 b 3 .
3a 2b 4ab 2 b 3 is a polynomial.
2ab 2 is a monomial.
2ab 2 3a 2b 4ab 2 b 3 2ab 2 3a 2b 2ab 2 4ab 2 2ab 2 b 3 Distribute 2ab 2.
2 3 a a 2 b 2 b 2 4 a a b 2 b 2 2 1 a b 2 b 3 Group like terms.
6a 3b 3 8a 2b 4 2ab 5
Multiply.
Remember: Add the exponents of
like bases to multiply.
Find each product.
2
2
1. 4x x 2x 3 2. c 2d 2 3c 2 cd 7d 2 4x 2 x 2 4x 2 2x 4x 2 3 c 2d 2 3c 2 c 2d 2 cd c 2d 2 7d 2 4x 2 x 2 4 2 x 2 x 4 3 x 2
3 c 2 c 2 d 2 c 2 c d 2 d 2
2
2
7c d d 4x 4 ⫹ 8x 3 ⫺ 12x 2
3c 4d 2 ⫺ c 3d 3 ⫹ 7c 2d 4
4. 3a 2b 2 8a 2 2ab b 2 3. 5xy 2 x 3 4x 2 2 2
2
2
2
5xy x3 5xy 4x 5xy 2 3a 2b 2 8a 2 3a 2b 2 2ab 2 2
2
3a b b 5 x ⭈ x 3 y 2 ⫹ 5 4 x ⭈ x 2 y 2 ⫹
2
5 2 xy
3 8 a 2 ⭈ a 2 b 2⫹ 3 ⫺2 a 2 ⭈ a b 2 ⭈ b ⫹ 3 ⫺1 a 2 b 2 ⭈ b 2 2
5x 4y 2 ⫹ 20x 3y 2 ⫹ 10xy 2
24a 4b ⫺ 6a 3b 3 ⫺ 3a 2b 4
5. 2y 3 y 2 9y 4 6. x 2y 2 4x 2 7y 2y 3 y 2 ⫹ 2y 3 ⫺9y ⫹ 2y 3 4 x 2y 2 4x 2 ⫹ x 2y 2 7y ;
2 y 3 ⭈ y 2 ⫹ 2 ⫺9 y 3 ⭈ y ⫹
3
2 4 y
4 x 2 ⭈ x 2 y 2 ⫹ 7x 2 y 2 ⭈ y
2y 5 ⫺ 18y 4 ⫹ 8y 3
4x 4y 2 ⫹ 7x 2y 3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-2_rt.indd 14
14
Holt Algebra 2
5/15/06 2:05:17 PM
Process Black
Name
Date
Class
Reteach
LESSON
6-2
Multiplying Polynomials (continued)
Use the Distributive Property to multiply two polynomials.
Distribute each term of the first polynomial to each term of the second polynomial.
2
Multiply: x 2 4x 3x 1 .
2
Horizontal Method: x 2 4x 3x 1 Distribute x to each term
of (4x 2 3x 1).
Distribute 2 to each term
of (4x 2 3x 1).
[ x 4x 2 x 3x x 1 ] [ 2 4x 2 2 3x 2 1 ]
3
2
2
4x 3x x 8x 6x 2
Multiply.
3
2
2
4x 3x 8x x 6x 2
Group like terms.
3
2
4x 5x 7x 2
Combine like terms.
4x 2 3x
x
2
8x 6x
3
4x 3x 2 x
4x 3 5x 2 7x
Vertical Method:
Align like terms.
Combine like
terms.
1
2
2
Multiply 4x 2 3x 1 by 2.
2
Multiply 4x 2 3x 1 by x.
Use the horizontal method to find each product.
8. a b a 2 ab 4b 7. x 3 x 2 2x 2 x x 2 x 2x x 2 3 x 2 3 2x 3 2 a a 2 ⫹ a ab ⫹ a ⫺4b ⫹ b
a 2 ⫹ b ab ⫹ b ⫺4b 3
2
2
2
x ⫺ 2x ⫹ 2x ⫺ 3x ⫹ 6x ⫺ 6
a ⫹ a b ⫺ 4ab ⫹ a b ⫹ ab ⫺
4b 2
x 3 ⫺ 5x 2 ⫹ 8x ⫺ 6
a 3 ⫹ 2a 2b ⫺ 4ab ⫹ ab 2 ⫺ 4b 2
3
2
2
Use the vertical method to find each product.
9. x 2 4x 6
10. y 2 3y 1
x2
y1
3
2
3
x ⫹ 6x ⫹ 2x ⫺ 12
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-2_rt.indd 15
2
y ⫺ 4y ⫹ 4y ⫺ 1
15
Holt Algebra 2
12/29/05 8:31:02 PM
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