7.4E: Exercises
- Page ID
- 30556
Practice Makes Perfect
Factor Perfect Square Trinomials
In the following exercises, factor.
\(16y^2+24y+9\)
- Answer
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\((4y+3)^2\)
\(25v^2+20v+4\)
\(36s^2+84s+49\)
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\((6s+7)^2\)
\(49s^2+154s+121\)
\(100x^2−20x+1\)
- Answer
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\((10x−1)^2\)
\(64z^2−16z+1\)
\(25n^2−120n+144\)
- Answer
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\((5n−12)^2\)
\(4p^2−52p+169\)
\(49x^2−28xy+4y^2\)
- Answer
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\((7x−2y)^2\)
\(25r^2−60rs+36s^2\)
\(25n^2+25n+4\)
- Answer
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\((5n+4)(5n+1)\)
\(100y^2−20y+1\)
\(64m^2−16m+1\)
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\((8m-1)^2\)
\(100x^2−25x+1\)
\(10k^2+80k+160\)
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\(10(k+4)^2\)
\(64x^2−96x+36\)
\(75u^3−30u^{2}v+3uv^2\)
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\(3u(5u−v)^2\)
\(90p^3+300p^{2}q+250pq^2\)
Factor Differences of Squares
In the following exercises, factor.
\(x^2−16\)
- Answer
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\((x−4)(x+4)\)
\(n^2−9\)
\(25v^2−1\)
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\((5v−1)(5v+1)\)
\(169q^2−1\)
\(121x^2−144y^2\)
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\((11x−12y)(11x+12y)\)
\(49x^2−81y^2\)
\(169c^2−36d^2\)
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\((13c−6d)(13c+6d)\)
\(36p^2−49q^2\)
\(4−49x^2\)
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\((2−7x)(2+7x)\)
\(121−25s^2\)
\(16z^4−1\)
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\((2z−1)(2z+1)(4z^2+1)\)
\(m^4−n^4\)
\(5q^2−45\)
- Answer
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\(5(q−3)(q+3)\)
\(98r^3−72r\)
\(24p^2+54\)
- Answer
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\(6(4p^2+9)\)
\(20b^2+140\)
Factor Sums and Differences of Cubes
In the following exercises, factor.
\(x^3+125\)
- Answer
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\((x+5)(x^2−5x+25)\)
\(n^3+512\)
\(z^3−27\)
- Answer
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\((z−3)(z^2+3z+9)\)
\(v^3−216\)
\(8−343t^3\)
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\((2−7t)(4+14t+49t^2)\)
\(125−27w^3\)
\(8y^3−125z^3\)
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\((2y−5z)(4y^2+10yz+25z^2)\)
\(27x^3−64y^3\)
\(7k^3+56\)
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\(7(k+2)(k^2−2k+4)\)
\(6x^3−48y^3\)
\(2−16y^3\)
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\(2(1−2y)(1+2y+4y^2)\)
\(−2x^3−16y^3\)
Mixed Practice
In the following exercises, factor.
\(64a^2−25\)
- Answer
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\((8a−5)(8a+5)\)
\(121x^2−144\)
\(27q^2−3\)
- Answer
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\(3(3q−1)(3q+1)\)
\(4p^2−100\)
\(16x^2−72x+81\)
- Answer
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\((4x−9)^2\)
\(36y^2+12y+1\)
\(8p^2+2\)
- Answer
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\(2(4p^2+1)\)
\(81x^2+169\)
\(125−8y^3\)
- Answer
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\((5−2y)(25+10y+4y^2)\)
\(27u^3+1000\)
\(45n^2+60n+20\)
- Answer
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\(5(3n+2)^2\)
\(48q^3−24q^2+3q\)
Everyday Math
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
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\((2w+15)^2\)
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
Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?
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Answers may vary.
How do you recognize the binomial squares pattern?
Explain why \(n^2+25 \ne (n+5)^2\).
- Answer
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Answers may vary.
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?