7.4E: Exercises
- Last updated
- Jan 6, 2020
- Save as PDF
- Page ID
- 30556
( \newcommand{\kernel}{\mathrm{null}\,}\)
Practice Makes Perfect
Factor Perfect Square Trinomials
In the following exercises, factor.
Exercise 1
16y2+24y+9
- Answer
-
(4y+3)2
Exercise 2
25v2+20v+4
Exercise 3
36s2+84s+49
- Answer
-
(6s+7)2
Exercise 4
49s2+154s+121
Exercise 5
100x2−20x+1
- Answer
-
(10x−1)2
Exercise 6
64z2−16z+1
Exercise 7
25n2−120n+144
- Answer
-
(5n−12)2
Exercise 8
4p2−52p+169
Exercise 9
49x2−28xy+4y2
- Answer
-
(7x−2y)2
Exercise 10
25r2−60rs+36s2
Exercise 11
25n2+25n+4
- Answer
-
(5n+4)(5n+1)
Exercise 12
100y2−20y+1
Exercise 13
64m2−16m+1
- Answer
-
(8m−1)2
Exercise 14
100x2−25x+1
Exercise 15
10k2+80k+160
- Answer
-
10(k+4)2
Exercise 16
64x2−96x+36
Exercise 17
75u3−30u2v+3uv2
- Answer
-
3u(5u−v)2
Exercise 18
90p3+300p2q+250pq2
Factor Differences of Squares
In the following exercises, factor.
Exercise 19
x2−16
- Answer
-
(x−4)(x+4)
Exercise 20
n2−9
Exercise 21
25v2−1
- Answer
-
(5v−1)(5v+1)
Exercise 22
169q2−1
Exercise 23
121x2−144y2
- Answer
-
(11x−12y)(11x+12y)
Exercise 24
49x2−81y2
Exercise 25
169c2−36d2
- Answer
-
(13c−6d)(13c+6d)
Exercise 26
36p2−49q2
Exercise 27
4−49x2
- Answer
-
(2−7x)(2+7x)
Exercise 28
121−25s2
Exercise 29
16z4−1
- Answer
-
(2z−1)(2z+1)(4z2+1)
Exercise 30
m4−n4
Exercise 31
5q2−45
- Answer
-
5(q−3)(q+3)
Exercise 32
98r3−72r
Exercise 33
24p2+54
- Answer
-
6(4p2+9)
Exercise 34
20b2+140
Factor Sums and Differences of Cubes
In the following exercises, factor.
Exercise 35
x3+125
- Answer
-
(x+5)(x2−5x+25)
Exercise 36
n3+512
Exercise 37
z3−27
- Answer
-
(z−3)(z2+3z+9)
Exercise 38
v3−216
Exercise 39
8−343t3
- Answer
-
(2−7t)(4+14t+49t2)
Exercise 40
125−27w3
Exercise 41
8y3−125z3
- Answer
-
(2y−5z)(4y2+10yz+25z2)
Exercise 42
27x3−64y3
Exercise 43
7k3+56
- Answer
-
7(k+2)(k2−2k+4)
Exercise 44
6x3−48y3
Exercise 45
2−16y3
- Answer
-
2(1−2y)(1+2y+4y2)
Exercise 46
−2x3−16y3
Mixed Practice
In the following exercises, factor.
Exercise 47
64a2−25
- Answer
-
(8a−5)(8a+5)
Exercise 48
121x2−144
Exercise 49
27q2−3
- Answer
-
3(3q−1)(3q+1)
Exercise 50
4p2−100
Exercise 51
16x2−72x+81
- Answer
-
(4x−9)2
Exercise 52
36y2+12y+1
Exercise 53
8p2+2
- Answer
-
2(4p2+1)
Exercise 54
81x2+169
Exercise 55
125−8y3
- Answer
-
(5−2y)(25+10y+4y2)
Exercise 56
27u3+1000
Exercise 57
45n2+60n+20
- Answer
-
5(3n+2)2
Exercise 58
48q3−24q2+3q
Everyday Math
Exercise 59
Landscaping Sue and Alan are planning to put a 15 foot square swimming pool in their backyard. They will surround the pool with a tiled deck, the same width on all sides. If the width of the deck is w, the total area of the pool and deck is given by the trinomial 4w2+60w+225.
- Answer
-
(2w+15)2
Exercise 60
Home repair The height a twelve foot ladder can reach up the side of a building if the ladder’s base is b feet from the building is the square root of the binomial 144−b2.
Writing Exercises
Exercise 61
Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?
- Answer
-
Answers may vary.
Exercise 62
How do you recognize the binomial squares pattern?
Exercise 63
Explain why n2+25≠(n+5)2.
- Answer
-
Answers may vary.
Exercise 64
Maribel factored y2−30y+81 as (y−9)^2. How do you know that this is incorrect?
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?