8-4 Special Product and Factoring:
(a ⫾ b)2 a2 ⫾ 2ab b2
Name
Date
Evaluate: (3m 8)2
Square the
first term.
Twice the product
of the terms
Remember:
The square of a binomial is the
square of the first term, plus
or minus twice the product of
both its terms, plus the square
of the last term.
Square the
last term.
(3m)2
2(3m)(8)
(8)2
9m2
48m
64
(a b)2 a2 2ab b2
(a b)2 a2 2ab b2
So (3m 8)2 9m2 48m 64.
Determine if 49q2 28q 16 is a perfect square trinomial.
49q2 28q 16
7q • 7q 2(7q)(4) 4 • 4
Think
Write the trinomial in the form a2 2ab b2,
where a 7q, and b 4.
?
2(7q)(4) 28q
56q 28q False
So 49q2 28q 16 is not a perfect square trinomial.
Square each binomial.
2. (r 20)2
1. (x 15)2
(x)2 2(x)(15) (15)2
Copyright © by William H. Sadlier, Inc. All rights reserved.
x2
(r)2 2(r)(20) (20)2
30x 225
5. (2x 11)2
r2
9h2
90xy 12h 4
10. (7u 3v)2
(5x)2 2(5x)(9y) (9y)2
81y2
42uv t2
y2 50y 625
28t 196
8. (8g 3)2
(8g)2 2(8g)(3) (3)2
(7b)2 2(7b)(5) (5)2
49b2
64g2 48g 9
70b 25
9v2
12. (12a 5b)2
(11r)2 2(11r)(7s) (7s)2 (12a)2 2(12a)(5b) (5b)2
121r 2 154rs 49s2
144a2 120ab 25b2
14. (0.5q 0.4r)2
13. (0.2x 0.3y)2
(y)2 2(y)(25) (25)2
(t)2 2(t)(14) (14)2
11. (11r 7s)2
(7u)2 2(7u)(3v) (3v)2
49u2
4. (y 25)2
7. (7b 5)2
(3h)2 2(3h)(2) (2)2
44x 121
9. (5x 9y)2
25x2
40r 400
6. (3h 2)2
(2x)2 2(2x)(11) (11)2
4x2
3. (t 14)2
1
2
(0.2x)2 2(0.2x)(0.3y) (0.3y)2
0.04x2
0.12xy 0.09y2
(0.5q)2 2(0.5q)(0.4r) (0.4r)2
0.25q2 0.4qr 0.16r 2
Lesson 8-4, pages 210–211.
2
1
15. ( 3 d 5 e)
(13d)
2
(13d)(15e) (15e)
2
1 2
2
1 2
d 15
de 25
e
9
Chapter 8
201
For More Practice Go To:
Determine if each trinomial is a perfect square. If so, factor it.
If not, explain why not.
11b • 11b 2(11b)(1) 1 • 1
?
2(11b)(1) 22b
22b 22b True
(11b 1)2
19. 49g2 56g 64
7g • 7g 2(7g)(8) 8 • 8
?
2(7g)(8) 56g
112g 56g False
not a perfect square
22. 25x2 110xy 121y2
5x • 5x 2(5x)(11y) 11y • 11y
?
2(5x)(11y) 110xy
110xy 110xy True
(5x – 11y)2
25. y2 1.2y 0.36
y • y 2(y)(0.6) 0.6 • 0.6
?
17. 64x2 16x 1
8x • 8x 2(8x)(1) 1 • 1
?
2(8x)(1) 16x
16x 16x True
not a perfect square
20. 16t 2 40t 25
21. 36r 2 84r 49
4t • 4t 2(4t)(5) 5 • 5
6r • 6r 2(6r)(7) 7 • 7
2(4t)(5) 40t
40t 40t True
2(6r)(7) 84r
84r 84r True
?
?
(4t 5)2
(6r – 7)2
23. 81v2 90vw 25w2
24. m2 m 0.25
m • m 2(m)(0.5) 0.5 • 0.5
9v • 9v 2(9v)(5w) 5w • 5w
?
2(9v)(5w) 90vw
90vw 90vw True
?
2(m)(0.5) m
m m True
(9v 5w)2
3
(m 0.5)2
9
10
26. q2 2 q 16
3
3
3
q • q 2(q)( ) ( ) • ( )
4
4
4
(y 0.6)2
Solve. Show your work.
2(q)
4x2 52x 169 s2
4x2 52x 169 2x • 2x – 2(2x)(13) 132,
if 2(2x)(13) 52x; 2(2x)(13) 52x,
so 2x • 2x 2(2x)(13) 132 (2x 13)2 s2
s (2x 13); The measure of each side of the
square is (2x 13).
30. Which trinomial is a perfect square?
(59) ? 109z
2(z)
3
3
q q True
2
2
2
q 34
(
10
10
z z True
9
9
5 2
z9
)
(
Chapter 8
)
29. Nancy is making a square garden with side
23v 4w. What trinomial represents the area
of the garden?
A s2; Let s 23v – 4w
so A (23v 4w)2 (23v)2 2(23v)(4w) (4w)2 529v2 184vw 16w2
So the trinomial 529v2 184vw 16w2
represents the area of Nancy’s square garden.
1
2
2
31. Evaluate: ( 2 x 5 y)
4
F. x2 5 y2
4
G. x2 5 y2
1
1
4
1
2
4
H. 4 x2 5 xy 25 y2
J. 4 x2 5 xy 25 y2
202
25
27. z2 9 z 81
5
5
5
z • z 2(z)( ) ( ) • ( )
9
9
9
(34) ? 32q
28. The trinomial 4x2 52x 169 represents the
area of a square. What binomial represents the
measure of each side of the square?
B. 81x2 126x 49
C. 100x2 100x 81
D. 36x2 25x 64
6c • 6c 2(6c)(5) 5 • 5
?
2(6c)(5) 30c
60c 30c False
(8x 1)2
2(y)(0.6) 1.2y
1.2y 1.2y True
A. 16x2 150x 625
18. 36c2 30c 25
Copyright © by William H. Sadlier, Inc. All rights reserved.
16. 121b2 22b 1