Name
Date
Class
Reteach
LESSON
7-8
Special Products of Binomials
A perfect-square trinomial is a trinomial that is the result of squaring a binomial.
a ⫹ b 2 ⫽ a 2 ⫹ 2ab ⫹ b 2
Square a.
Square b.
Add product of 2, a, and b.
a ⫺ b 2 ⫽ a 2 ⫺ 2ab ⫹ b 2
Square a.
Square b.
Subtract product of 2, a, and b.
Multiply x ⫹ 4 2.
Multiply 4x ⫺ 3 2.
a: x
b: 4
4x ⫺ 3 2
a:
b:
x 2 ⫹ 2 x 4 ⫹ 4 2
Middle term is added.
16x 2 ⫺ 2 4x 3 ⫹ 3 2
x ⫹ 8x ⫹ 16
Simplify.
Middle term is
subtracted.
16x 2 ⫺ 24x ⫹ 9
Simplify.
x
⫹ 4 2
2
4x
3
State whether each product will result in a perfect-square trinomial.
1.
x ⫹ 5 x ⫹ 5 2. x ⫹ 2 x ⫺ 2 yes
3. 5x ⫺ 6 5x ⫺ 6 no
yes
Fill in the blanks. Then write the perfect-square trinomial.
4.
x
⫹ 7 2
5. x ⫺ 1 2
Square a:
x
2 a b :
Square b:
6. 2x ⫹ 10 2
2
2
4x
2x
2 a b :
40x
1
Square b:
100
x
14x
2 a b :
49
Square b:
x 2 ⫹ 14x ⫹ 49
2
Square a:
Square a:
x 2 ⫺ 2x ⫹ 1
4x 2 ⫹ 40x ⫹ 100
Multiply.
7.
x ⫺ 8 2
2
8. x ⫹ 2 x 2 ⫺ 16x ⫹ 64
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c07-8_rt.indd 62
2
9. 7x ⫺ 5 x 2 ⫹ 4x ⫹ 4
62
49x 2 ⫺ 70x ⫹ 25
Holt Algebra 1
12/26/05 7:58:29 AM
Process Black
Name
LESSON
7-8
Date
Class
Reteach
Special Products of Binomials (continued)
When you multiply certain types of binomials, the middle term will be zero.
Multiply a ⫹ b a ⫺ b .
a ⫹ b a ⫺ b a a ⫺ b ⫹ b a ⫺ b a ⫺ ab ⫹ ab ⫺ b
2
Distribute.
2
a2 ⫺ b2
Combine like terms.
This type of special product is called a difference of squares.
a ⫹ b a ⫺ b ⫽ a 2 ⫺ b 2
Square b.
Square a.
Subtract.
Multiply x ⫹ 4 x ⫺ 4 .
x
⫹ 4 x ⫺ 4 Multiply 7 ⫹ 8x 7 ⫺ 8x .
7 ⫹ 8x 7 ⫺ 8x a: x
b: 4
x 2 ⫺ 4 2
7 2
x 2 ⫺ 16
⫺ 8x 2
49 ⫺ 64x 2
Simplify.
a: 7
b: 8x
Simplify.
State whether the products will form a difference of squares or a
perfect-square trinomial.
10. x ⫹ 10 x ⫺ 10 difference of squares
11. y ⫹ 6 y ⫹ 6 12. z ⫺ 3 z ⫺ 3 perfect-square trinomial
perfect-square trinomial
Fill in the blanks. Then write the difference of squares.
13. a ⫹ 7 a ⫺ 7 14. 2 ⫹ m 2 ⫺ m 15. 2x ⫹ 5 2x ⫺ 5 Square a:
a2
Square a:
4
Square a:
4x 2
Square b:
49
Square b:
m2
Square b:
25
a 2 ⫺ 49
4 ⫺ m2
4x 2 ⫺ 25
Multiply.
16. x ⫹ 8 x ⫺ 8 2
x ⫺ 64
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c07-8_rt.indd 63
17. 10 ⫹ x 10 ⫺ x 100 ⫺ x
63
2
18. 5x ⫹ 2y 5x ⫺ 2y 2
25x ⫺ 4y
2
Holt Algebra 1
12/26/05 7:58:30 AM
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