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6.3 Factor Special Products

Recognizing perfect square trinomials, differences of squares, and sums or differences of cubes so the factors follow from a memorized pattern.

Intermediate Algebra 2e, 6.3 Factor Special Products

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66 exercises

6.3 Exercise 1

Before you get started, take this readiness quiz.

Simplify: (3x2)3.\left(3 x^{2}\right)^{3} .
If you missed this problem, review the reference.

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6.3 Exercise 2

Multiply: (m+4)2.\left(m + 4\right)^{2} .
If you missed this problem, review the reference.

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6.3 Exercise 3

Multiply: (x−3)(x+3).\left(x - 3\right) \left(x + 3\right) .
If you missed this problem, review the reference.

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6.3 Exercise 5

Factor: 4x2+12x+9.4 x^{2} + 12 x + 9 .

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6.3 Exercise 6

Factor: 9y2+24y+16.9 y^{2} + 24 y + 16 .

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6.3 Exercise 8

Factor: 64y2−80y+25.64 y^{2} - 80 y + 25 .

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6.3 Exercise 9

Factor: 16z2−72z+81.16 z^{2} - 72 z + 81 .

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6.3 Exercise 11

Factor: 49x2+84xy+36y2.49 x^{2} + 84 x y + 36 y^{2} .

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6.3 Exercise 12

Factor: 64m2+112mn+49n2.64 m^{2} + 112 m n + 49 n^{2} .

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6.3 Exercise 14

Factor: 8x2y−24xy+18y.8 x^{2} y - 24 x y + 18 y .

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6.3 Exercise 15

Factor: 27p2q+90pq+75q.27 p^{2} q + 90 p q + 75 q .

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6.3 Exercise 17

Factor: 121m2−1.121 m^{2} - 1 .

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6.3 Exercise 18

Factor: 81y2−1.81 y^{2} - 1 .

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6.3 Exercise 19

Factor: 144x2−49y2.144 x^{2} - 49 y^{2} .

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6.3 Exercise 20

Factor: 196m2−25n2.196 m^{2} - 25 n^{2} .

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6.3 Exercise 21

Factor: 121p2−9q2.121 p^{2} - 9 q^{2} .

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6.3 Exercise 22

Factor: 48x4y2−243y2.48 x^{4} y^{2} - 243 y^{2} .

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6.3 Exercise 23

Factor: 2x4y2−32y2.2 x^{4} y^{2} - 32 y^{2} .

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6.3 Exercise 24

Factor: 7a4c2−7b4c2.7 a^{4} c^{2} - 7 b^{4} c^{2} .

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6.3 Exercise 26

Factor: x2−10x+25−y2.x^{2} - 10 x + 25 - y^{2} .

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6.3 Exercise 27

Factor: x2+6x+9−4y2.x^{2} + 6 x + 9 - 4 y^{2} .

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6.3 Exercise 29

Factor: x3+27.x^{3} + 27 .

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6.3 Exercise 30

Factor: y3+8.y^{3} + 8 .

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6.3 Exercise 32

Factor: 8x3−27y3.8 x^{3} - 27 y^{3} .

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6.3 Exercise 33

Factor: 1000m3−125n3.1000 m^{3} - 125 n^{3} .

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6.3 Exercise 35

Factor: 500p3+4q3.500 p^{3} + 4 q^{3} .

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6.3 Exercise 36

Factor: 432c3+686d3.432 c^{3} + 686 d^{3} .

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6.3 Exercise 38

Factor: (y+1)3−27y3.\left(y + 1\right)^{3} - 27 y^{3} .

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6.3 Exercise 39

Factor: (n+3)3−125n3.\left(n + 3\right)^{3} - 125 n^{3} .

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6.3 Exercise 40

Factor completely using the perfect square trinomials pattern.

16y2+24y+916 y^{2} + 24 y + 9

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6.3 Exercise 42

Factor completely using the perfect square trinomials pattern.

36s2+84s+4936 s^{2} + 84 s + 49

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6.3 Exercise 44

Factor completely using the perfect square trinomials pattern.

100x2−20x+1100 x^{2} - 20 x + 1

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6.3 Exercise 46

Factor completely using the perfect square trinomials pattern.

25n2−120n+14425 n^{2} - 120 n + 144

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6.3 Exercise 48

Factor completely using the perfect square trinomials pattern.

49x2+28xy+4y249 x^{2} + 28 x y + 4 y^{2}

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6.3 Exercise 50

Factor completely using the perfect square trinomials pattern.

100y2−20y+1100 y^{2} - 20 y + 1

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6.3 Exercise 52

Factor completely using the perfect square trinomials pattern.

10jk2+80jk+160j10 j k^{2} + 80 j k + 160 j

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6.3 Exercise 54

Factor completely using the perfect square trinomials pattern.

75u4−30u3v+3u2v275 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}

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6.3 Exercise 56

Factor completely using the difference of squares pattern, if possible.

25v2−125 v^{2} - 1

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6.3 Exercise 58

Factor completely using the difference of squares pattern, if possible.

4−49x24 - 49 x^{2}

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6.3 Exercise 60

Factor completely using the difference of squares pattern, if possible.

6p2q2−54p26 p^{2} q^{2} - 54 p^{2}

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6.3 Exercise 62

Factor completely using the difference of squares pattern, if possible.

24p2+5424 p^{2} + 54

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6.3 Exercise 64

Factor completely using the difference of squares pattern, if possible.

121x2−144y2121 x^{2} - 144 y^{2}

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6.3 Exercise 66

Factor completely using the difference of squares pattern, if possible.

169c2−36d2169 c^{2} - 36 d^{2}

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6.3 Exercise 68

Factor completely using the difference of squares pattern, if possible.

16z4−116 z^{4} - 1

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6.3 Exercise 70

Factor completely using the difference of squares pattern, if possible.

162a4b2−32b2162 a^{4} b^{2} - 32 b^{2}

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6.3 Exercise 72

Factor completely using the difference of squares pattern, if possible.

x2−16x+64−y2x^{2} - 16 x + 64 - y^{2}

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6.3 Exercise 74

Factor completely using the difference of squares pattern, if possible.

a2+6a+9−9b2a^{2} + 6 a + 9 - 9 b^{2}

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6.3 Exercise 76

Factor completely using the sums and differences of cubes pattern, if possible.

x3+125x^{3} + 125

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6.3 Exercise 78

Factor completely using the sums and differences of cubes pattern, if possible.

z6−27z^{6} - 27

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6.3 Exercise 80

Factor completely using the sums and differences of cubes pattern, if possible.

8−343t38 - 343 t^{3}

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6.3 Exercise 82

Factor completely using the sums and differences of cubes pattern, if possible.

8y3−125z38 y^{3} - 125 z^{3}

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6.3 Exercise 84

Factor completely using the sums and differences of cubes pattern, if possible.

216a3+125b3216 a^{3} + 125 b^{3}

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6.3 Exercise 86

Factor completely using the sums and differences of cubes pattern, if possible.

7k3+567 k^{3} + 56

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6.3 Exercise 88

Factor completely using the sums and differences of cubes pattern, if possible.

2x2−16x2y32 x^{2} - 16 x^{2} y^{3}

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6.3 Exercise 90

Factor completely using the sums and differences of cubes pattern, if possible.

(x+3)3+8x3\left(x + 3\right)^{3} + 8 x^{3}

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6.3 Exercise 92

Factor completely using the sums and differences of cubes pattern, if possible.

(y−5)3−64y3\left(y - 5\right)^{3} - 64 y^{3}

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6.3 Exercise 94

Factor completely.

64a2−2564 a^{2} - 25

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6.3 Exercise 96

Factor completely.

27q2−327 q^{2} - 3

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6.3 Exercise 98

Factor completely.

16x2−72x+8116 x^{2} - 72 x + 81

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6.3 Exercise 100

Factor completely.

8p2+28 p^{2} + 2

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6.3 Exercise 102

Factor completely.

125−8y3125 - 8 y^{3}

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6.3 Exercise 104

Factor completely.

45n2+60n+2045 n^{2} + 60 n + 20

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6.3 Exercise 106

Factor completely.

x2−10x+25−y2x^{2} - 10 x + 25 - y^{2}

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6.3 Exercise 108

Factor completely.

(x+1)3+8x3\left(x + 1\right)^{3} + 8 x^{3}

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6.3 Exercise 110

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

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6.3 Exercise 112

Explain why n2+25≠(n+5)2.n^{2} + 25 \neq \left(n + 5\right)^{2} . Use algebra, words, or pictures.

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Adapted from Intermediate Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Intermediate Algebra 2e. Imported at revision 77a933c.