7.4E: Exercises
- Page ID
- 30556
Practice Makes Perfect
Factor Perfect Square Trinomials
In the following exercises, factor.
Exercise 1
\(16y^2+24y+9\)
- Answer
-
\((4y+3)^2\)
Exercise 2
\(25v^2+20v+4\)
Exercise 3
\(36s^2+84s+49\)
- Answer
-
\((6s+7)^2\)
Exercise 4
\(49s^2+154s+121\)
Exercise 5
\(100x^2−20x+1\)
- Answer
-
\((10x−1)^2\)
Exercise 6
\(64z^2−16z+1\)
Exercise 7
\(25n^2−120n+144\)
- Answer
-
\((5n−12)^2\)
Exercise 8
\(4p^2−52p+169\)
Exercise 9
\(49x^2−28xy+4y^2\)
- Answer
-
\((7x−2y)^2\)
Exercise 10
\(25r^2−60rs+36s^2\)
Exercise 11
\(25n^2+25n+4\)
- Answer
-
\((5n+4)(5n+1)\)
Exercise 12
\(100y^2−20y+1\)
Exercise 13
\(64m^2−16m+1\)
- Answer
-
\((8m-1)^2\)
Exercise 14
\(100x^2−25x+1\)
Exercise 15
\(10k^2+80k+160\)
- Answer
-
\(10(k+4)^2\)
Exercise 16
\(64x^2−96x+36\)
Exercise 17
\(75u^3−30u^{2}v+3uv^2\)
- Answer
-
\(3u(5u−v)^2\)
Exercise 18
\(90p^3+300p^{2}q+250pq^2\)
In the following exercises, factor.
Exercise 19
\(x^2−16\)
- Answer
-
\((x−4)(x+4)\)
Exercise 20
\(n^2−9\)
Exercise 21
\(25v^2−1\)
- Answer
-
\((5v−1)(5v+1)\)
Exercise 22
\(169q^2−1\)
Exercise 23
\(121x^2−144y^2\)
- Answer
-
\((11x−12y)(11x+12y)\)
Exercise 24
\(49x^2−81y^2\)
Exercise 25
\(169c^2−36d^2\)
- Answer
-
\((13c−6d)(13c+6d)\)
Exercise 26
\(36p^2−49q^2\)
Exercise 27
\(4−49x^2\)
- Answer
-
\((2−7x)(2+7x)\)
Exercise 28
\(121−25s^2\)
Exercise 29
\(16z^4−1\)
- Answer
-
\((2z−1)(2z+1)(4z^2+1)\)
Exercise 30
\(m^4−n^4\)
Exercise 31
\(5q^2−45\)
- Answer
-
\(5(q−3)(q+3)\)
Exercise 32
\(98r^3−72r\)
Exercise 33
\(24p^2+54\)
- Answer
-
\(6(4p^2+9)\)
Exercise 34
\(20b^2+140\)
Factor Sums and Differences of Cubes
In the following exercises, factor.
Exercise 35
\(x^3+125\)
- Answer
-
\((x+5)(x^2−5x+25)\)
Exercise 36
\(n^3+512\)
Exercise 37
\(z^3−27\)
- Answer
-
\((z−3)(z^2+3z+9)\)
Exercise 38
\(v^3−216\)
Exercise 39
\(8−343t^3\)
- Answer
-
\((2−7t)(4+14t+49t^2)\)
Exercise 40
\(125−27w^3\)
Exercise 41
\(8y^3−125z^3\)
- Answer
-
\((2y−5z)(4y^2+10yz+25z^2)\)
Exercise 42
\(27x^3−64y^3\)
Exercise 43
\(7k^3+56\)
- Answer
-
\(7(k+2)(k^2−2k+4)\)
Exercise 44
\(6x^3−48y^3\)
Exercise 45
\(2−16y^3\)
- Answer
-
\(2(1−2y)(1+2y+4y^2)\)
Exercise 46
\(−2x^3−16y^3\)
Mixed Practice
In the following exercises, factor.
Exercise 47
\(64a^2−25\)
- Answer
-
\((8a−5)(8a+5)\)
Exercise 48
\(121x^2−144\)
Exercise 49
\(27q^2−3\)
- Answer
-
\(3(3q−1)(3q+1)\)
Exercise 50
\(4p^2−100\)
Exercise 51
\(16x^2−72x+81\)
- Answer
-
\((4x−9)^2\)
Exercise 52
\(36y^2+12y+1\)
Exercise 53
\(8p^2+2\)
- Answer
-
\(2(4p^2+1)^2\)
Exercise 54
\(81x^2+169\)
Exercise 55
\(125−8y^3\)
- Answer
-
\((5−2y)(25+10y+4y^2)\)
Exercise 56
\(27u^3+1000\)
Exercise 57
\(45n^2+60n+20\)
- Answer
-
\(5(3n+2)^2\)
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 \(4w^2+60w+225\).
- 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 \(144−b^2\).
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 \(n^2+25 \ne (n+5)^2\).
- Answer
-
Answers may vary.
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?