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7.4E: Exercises

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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

100x220x+1

Answer

(10x1)2

Exercise 6

64z216z+1

Exercise 7

25n2120n+144

Answer

(5n12)2

Exercise 8

4p252p+169

Exercise 9

49x228xy+4y2

Answer

(7x2y)2

Exercise 10

25r260rs+36s2

Exercise 11

25n2+25n+4

Answer

(5n+4)(5n+1)

Exercise 12

100y220y+1

Exercise 13

64m216m+1

Answer

(8m1)2

Exercise 14

100x225x+1

Exercise 15

10k2+80k+160

Answer

10(k+4)2

Exercise 16

64x296x+36

Exercise 17

75u330u2v+3uv2

Answer

3u(5uv)2

Exercise 18

90p3+300p2q+250pq2

​​​​​​Factor Differences of Squares

In the following exercises, factor.

Exercise 19

x216

Answer

(x4)(x+4)

Exercise 20

n29

Exercise 21

25v21

Answer

(5v1)(5v+1)

Exercise 22

169q21

Exercise 23

121x2144y2

Answer

(11x12y)(11x+12y)

Exercise 24

49x281y2

Exercise 25

169c236d2

Answer

(13c6d)(13c+6d)

Exercise 26

36p249q2

Exercise 27

449x2

Answer

(27x)(2+7x)

Exercise 28

12125s2

Exercise 29

16z41

Answer

(2z1)(2z+1)(4z2+1)

Exercise 30

m4n4

Exercise 31

5q245

Answer

5(q3)(q+3)

Exercise 32

98r372r

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)(x25x+25)

Exercise 36

n3+512

Exercise 37

z327

Answer

(z3)(z2+3z+9)

Exercise 38

v3216

Exercise 39

8343t3

Answer

(27t)(4+14t+49t2)

Exercise 40

12527w3

Exercise 41

8y3125z3

Answer

(2y5z)(4y2+10yz+25z2)

Exercise 42

27x364y3

Exercise 43

7k3+56

Answer

7(k+2)(k22k+4)

Exercise 44

6x348y3

Exercise 45

216y3

Answer

2(12y)(1+2y+4y2)

Exercise 46

2x316y3

Mixed Practice

In the following exercises, factor.

Exercise 47

64a225

Answer

(8a5)(8a+5)

Exercise 48

121x2144

Exercise 49

27q23

Answer

3(3q1)(3q+1)

Exercise 50

4p2100

Exercise 51

16x272x+81

Answer

(4x9)2

Exercise 52

36y2+12y+1

Exercise 53

8p2+2

Answer

2(4p2+1)

Exercise 54

81x2+169

Exercise 55

1258y3

Answer

(52y)(25+10y+4y2)

Exercise 56

27u3+1000

Exercise 57

45n2+60n+20

Answer

5(3n+2)2

Exercise 58

48q324q2+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 144b2.

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 y230y+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.

This table has the following statements all to be preceded by “I can…”. The first row is “factor perfect square trinomials”. The second row is “factor differences of squares”. The third row is “factor sums and differences of cubes”. In the columns beside these statements are the headers, “confidently”, “with some help”, and “no-I don’t get it!”.

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?


This page titled 7.4E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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