# 7.4E: Exercises

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## Practice Makes Perfect

Factor Perfect Square Trinomials

In the following exercises, factor.

##### Exercise 1

$$16y^2+24y+9$$

$$(4y+3)^2$$

##### Exercise 2

$$25v^2+20v+4$$

##### Exercise 3

$$36s^2+84s+49$$

$$(6s+7)^2$$

##### Exercise 4

$$49s^2+154s+121$$

##### Exercise 5

$$100x^2−20x+1$$

$$(10x−1)^2$$

##### Exercise 6

$$64z^2−16z+1$$

##### Exercise 7

$$25n^2−120n+144$$

$$(5n−12)^2$$

##### Exercise 8

$$4p^2−52p+169$$

##### Exercise 9

$$49x^2−28xy+4y^2$$

$$(7x−2y)^2$$

##### Exercise 10

$$25r^2−60rs+36s^2$$

##### Exercise 11

$$25n^2+25n+4$$

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

##### Exercise 12

$$100y^2−20y+1$$

##### Exercise 13

$$64m^2−16m+1$$

$$(8m-1)^2$$

##### Exercise 14

$$100x^2−25x+1$$

##### Exercise 15

$$10k^2+80k+160$$

$$10(k+4)^2$$

##### Exercise 16

$$64x^2−96x+36$$

##### Exercise 17

$$75u^3−30u^{2}v+3uv^2$$

$$3u(5u−v)^2$$

##### Exercise 18

$$90p^3+300p^{2}q+250pq^2$$

​​​​​​Factor Differences of Squares

In the following exercises, factor.

##### Exercise 19

$$x^2−16$$

$$(x−4)(x+4)$$

##### Exercise 20

$$n^2−9$$

##### Exercise 21

$$25v^2−1$$

$$(5v−1)(5v+1)$$

##### Exercise 22

$$169q^2−1$$

##### Exercise 23

$$121x^2−144y^2$$

$$(11x−12y)(11x+12y)$$

##### Exercise 24

$$49x^2−81y^2$$

##### Exercise 25

$$169c^2−36d^2$$

$$(13c−6d)(13c+6d)$$

##### Exercise 26

$$36p^2−49q^2$$

##### Exercise 27

$$4−49x^2$$

$$(2−7x)(2+7x)$$

##### Exercise 28

$$121−25s^2$$

##### Exercise 29

$$16z^4−1$$

$$(2z−1)(2z+1)(4z^2+1)$$

##### Exercise 30

$$m^4−n^4$$

##### Exercise 31

$$5q^2−45$$

$$5(q−3)(q+3)$$

##### Exercise 32

$$98r^3−72r$$

##### Exercise 33

$$24p^2+54$$

$$6(4p^2+9)$$

##### Exercise 34

$$20b^2+140$$

Factor Sums and Differences of Cubes

In the following exercises, factor.

##### Exercise 35

$$x^3+125$$

$$(x+5)(x^2−5x+25)$$

##### Exercise 36

$$n^3+512$$

##### Exercise 37

$$z^3−27$$

$$(z−3)(z^2+3z+9)$$

##### Exercise 38

$$v^3−216$$

##### Exercise 39

$$8−343t^3$$

$$(2−7t)(4+14t+49t^2)$$

##### Exercise 40

$$125−27w^3$$

##### Exercise 41

$$8y^3−125z^3$$

$$(2y−5z)(4y^2+10yz+25z^2)$$

##### Exercise 42

$$27x^3−64y^3$$

##### Exercise 43

$$7k^3+56$$

$$7(k+2)(k^2−2k+4)$$

##### Exercise 44

$$6x^3−48y^3$$

##### Exercise 45

$$2−16y^3$$

$$2(1−2y)(1+2y+4y^2)$$

##### Exercise 46

$$−2x^3−16y^3$$

Mixed Practice

In the following exercises, factor.

##### Exercise 47

$$64a^2−25$$

$$(8a−5)(8a+5)$$

##### Exercise 48

$$121x^2−144$$

##### Exercise 49

$$27q^2−3$$

$$3(3q−1)(3q+1)$$

##### Exercise 50

$$4p^2−100$$

##### Exercise 51

$$16x^2−72x+81$$

$$(4x−9)^2$$

##### Exercise 52

$$36y^2+12y+1$$

##### Exercise 53

$$8p^2+2$$

$$2(4p^2+1)$$

##### Exercise 54

$$81x^2+169$$

##### Exercise 55

$$125−8y^3$$

$$(5−2y)(25+10y+4y^2)$$

##### Exercise 56

$$27u^3+1000$$

##### Exercise 57

$$45n^2+60n+20$$

$$5(3n+2)^2$$

##### Exercise 58

$$48q^3−24q^2+3q$$

## 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 $$4w^2+60w+225$$.

$$(2w+15)^2$$

##### 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 $$144−b^2$$.

## Writing Exercises

##### Exercise 61

Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?

##### Exercise 62

How do you recognize the binomial squares pattern?

##### Exercise 63

Explain why $$n^2+25 \ne (n+5)^2$$.

##### Exercise 64

Maribel factored $$y^2−30y+81$$ 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?

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