4A.3E: Exercises
- Page ID
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Factor Perfect Square Trinomials
In the following exercises, factor completely using the perfect square trinomials pattern.
\(16y^2+24y+9\)
- Answer
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\((4y+3)^2\)
\(25v^2+20v+4\)
\(36s^2+84s+49\)
- Answer
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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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\((7x+2y)^2\)
\(25r^2+60rs+36s^2\)
\(100y^2−52y+1\)
- Answer
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\((50y−1)(2y−1)\)
\(64m^2−34m+1\)
\(10jk^2+80jk+160j\)
- Answer
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\(10j(k+4)^2\)
\(64x^2y−96xy+36y\)
\(75u^4−30u^3v+3u^2v^2\)
- Answer
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\(3u^2(5u−v)^2\)
\(90p^4+300p^4q+250p^2q^2\)
Factor Differences of Squares
In the following exercises, factor completely using the difference of squares pattern, if possible.
\(25v^2−1\)
- Answer
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\((5v−1)(5v+1)\)
\(169q^2−1\)
\(4−49x^2\)
- Answer
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\((7x−2)(7x+2)\)
\(121−25s^2\)
\(6p^2q^2−54p^2\)
- Answer
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\(6p^2(q−3)(q+3)\)
\(98r^3−72r\)
\(24p^2+54\)
- Answer
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\(6(4p^2+9)\)
\(20b^2+140\)
\(121x^2−144y^2\)
- Answer
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\((11x−12y)(11x+12y)\)
\(49x^2−81y^2\)
\(169c^2−36d^2\)
- Answer
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\((13c−6d)(13c+6d)\)
\(36p^2−49q^2\)
\(16z^4−1\)
- Answer
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\((2z−1)(2z+1)(4z^2+1)\)
\(m^4−n^4\)
\(162a^4b^2−32b^2\)
- Answer
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\(2b^2(3a−2)(3a+2)(9a^2+4)\)
\(48m^4n^2−243n^2\)
\(x^2−16x+64−y^2\)
- Answer
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\((x−8−y)(x−8+y)\)
\(p^2+14p+49−q^2\)
\(a^2+6a+9−9b^2\)
- Answer
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\((a+3−3b)(a+3+3b)\)
\(m^2−6m+9−16n^2\)
Factor Sums and Differences of Cubes
In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
\(x^3+125\)
- Answer
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\((x+5)(x^2−5x+25)\)
\(n^6+512\)
\(z^6−27\)
- Answer
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\((z^2−3)(z^4+3z^2+9)\)
\(v^3−216\)
\(8−343t^3\)
- Answer
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\((2−7t)(4+14t+49t^2)\)
\(125−27w^3\)
\(8y^3−125z^3\)
- Answer
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\((2y−5z)(4y^2+10yz+25z^2)\)
\(27x^3−64y^3\)
\(216a^3+125b^3\)
- Answer
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\((6a+5b)(36a^2−30ab+25b^2)\)
\(27y^3+8z^3\)
\(7k^3+56\)
- Answer
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\(7(k+2)(k^2−2k+4)\)
\(6x^3−48y^3\)
\(2x^2−16x^2y^3\)
- Answer
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\(2x^2(1−2y)(1+2y+4y^2)\)
\(−2x^3y^2−16y^5\)
\((x+3)^3+8x^3\)
- Answer
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\(9(x+1)(x^2+3)\)
\((x+4)^3−27x^3\)
\((y−5)^3−64y^3\)
- Answer
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\(−(3y+5)(21y^2−30y+25)\)
\((y−5)^3+125y^3\)
Mixed Practice
In the following exercises, factor completely.
\(64a^2−25\)
- 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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\(5(3n+2)^2\)
\(48q^3−24q^2+3q\)
\(x^2−10x+25−y^2\)
- Answer
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\((x+y−5)(x−y−5)\)
\(x^2+12x+36−y^2\)
\((x+1)^3+8x^3\)
- Answer
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\((3x+1)(3x^2+1)\)
\((y−3)^3−64y^3\)
Writing Exercises
Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?
- Answer
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Answers will vary.
How do you recognize the binomial squares pattern?
Explain why \(n^2+25\neq (n+5)^2\). Use algebra, words, or pictures.
- Answer
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Answers will vary.
Maribel factored \(y^2−30y+81\) as \((y−9)^2\). Was she right or wrong? How do you know?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?