Brain Busters Exercises 55 – 60 involve grouping symbols (Section 1.2),factoring by
grouping (Section 6.1),and factoring sums and differences of cubes (Section 6.4).Multiply or
divide as indicated. Write each answer in lowest terms.55.56.57.58.59.60.61.If the rational expression represents the area of a rectangle
and represents the length, what rational expression represents
the width?
62.Concept Check If you are given the following problem, what
must be the polynomial that is represented by the question mark?
4 y+ 12
2 y- 10
,?
y^2 - y- 20
=21 y+ 42
y- 32 xy
p5 x^2 y^3
2 pqb^3 - 8 a^3
4 a^3 + 4 a^2 b+ab^2,4 a^2 + 2 ab+b^2- a^3 - ab^3
- x^3 - y^3
x^2 - 2 xy+y^2
,
3 y^2 - 3 xy
x^2 - y^24 r^2 - t^2 + 10 r- 5 t
2 r^2 +rt+ 5 r#^4 r
(^3) + 4 r (^2) t+rt 2
2 r+t
3 a- 3 b-a^2 +b^2
4 a^2 - 4 ab+b^2
#^4 a
(^2) - b 2
2 a^2 - ab-b^2
m- 8
m- 4
,a
m^2 - 12 m+ 32
8 m
m
(^2) - 8 m
m^2 - 8 m+ 16
b
x+ 5
x+ 10
,a
x^2 + 10 x+ 25
x^2 + 10 x
#^10 x
x^2 + 15 x+ 50
b
1 x+ 4231 x- 32
x^2 - 9
,
x^2 + 8 x+ 16
x^2 + 6 x+ 9
1 q- 3241 q+ 22
q^2 + 3 q+ 2
,
q^2 - 6 q+ 9
q^2 + 4 q+ 4
m^2 + 8 mn+ 7 n^2
m^2 +mn- 42 n^2
,
m^2 - 3 mn- 4 n^2
m^2 - mn- 30 n^2
r^2 +rs- 12 s^2
r^2 - rs- 20 s^2
,
r^2 - 2 rs- 3 s^2
r^2 +rs- 30 s^2
6 s^2 + 17 s+ 10
s^2 - 4
s
(^2) - 2 s
6 s^2 + 29 s+ 20
2 m^2 + 7 m+ 3
m^2 - 9
m
(^2) - 3 m
2 m^2 + 11 m+ 5
r^2 +r- 6
r^2 + 4 r- 12
,
r+ 3
r- 1
y^2 +y- 2
y^2 + 3 y- 4
,
y+ 2
y+ 3
z^2 - z- 6
z^2 - 2 z- 8
#z
(^2) + 7 z+ 12
z^2 - 9
m^2 + 3 m+ 2
m^2 + 5 m+ 4
#m
(^2) + 10 m+ 24
m^2 + 5 m+ 6
r^2 +rs- 12 s^2
r^2 - rs- 20 s^2
,
r^2 - 2 rs- 3 s^2
r^2 +rs- 30 s^2
m^2 + 2 mp- 3 p^2
m^2 - 3 mp+ 2 p^2
,
m^2 + 4 mp+ 3 p^2
m^2 + 2 mp- 8 p^2
2 m^2 - 5 m- 12
m^2 - 10 m+ 24
m
(^2) - 9 m+ 18
4 m^2 - 9
2 k^2 + 3 k- 2
6 k^2 - 7 k+ 2
#^4 k
(^2) - 5 k+ 1
k^2 +k- 2
434 CHAPTER 7 Rational Expressions and Applications
Length =
Width
2 xy
p
5 x^2 y^3
The area is. 2 pq
Write the prime factored form of each number. See Section 1.1.
- 18 64. 48 65. 108 66. 60
Find the greatest common factor of each group of terms. See Section 6.1.- 24 m, 18m^2 , 6 68. 14 t^2 , 28t, 7 69. 84 q^3 , 90q^6 70. 54 k^3 , 36k^4
PREVIEW EXERCISES
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