﻿ FACTORING EXPRESSIONS WITH PERFECT CUBES

FACTORING EXPRESSIONS WITH PERFECT CUBES

Courtesy of Harold Hiken

Each of the following expressions is either a difference of perfect cubes or a sum of perfect cubes.  Factor appropriately.

1)      a3 + 1                                                         11)  27a3 – 64b3

2)      a3 – 1                                                         12)  125t3 + 8s3

3)      x3 – 8                                                         13)  27r3 + 1000s3

4)      m3 + 8                                                        14)  216z3 – w3

5)      p3 + q3                                                       15)  125m3 – 8p3

6)      k3 – h3                                                        16)  m6 – 8

7)      y3 – 8x3                                                      17)  64y6 + 1

8)      8p3 + q3                                                     18)  8k6 – 27q3

9)      64p3 + n3                                                    19)  125z3 + 64r6

10)  27x3 – 1                                                    20)  (a – b)3 – (a + b)3

1)      (a + 1)(a2 – a + 1)

2)      (a – 1)(a2 + a + 1)

3)      (x – 2)(x2 + 2x + 4)

4)      (m + 2)(m2 – 2m + 4)

5)      (p + q)(p2 – pq + q2)

6)      (k – h)(k2 + kh + h2)

7)      (y – 2x)(y2 + 2xy + 4x2)

8)      (2p + q)(4p2 – 2pq + q2)

9)      (4p + n)(16p2 – 4pn + n2)

10)  (3x – 1)(9x2 + 3x + 1)

11)  (3a – 4b)(9a2 + 12ab + 16b2)

12)  (5t + 2s)(25t2 – 10st + 4s2)

13)  (3r + 10s)(9r2 – 30rs + 100s2)

14)  (6z – w)(36z2 + 6zw + w2)

15)  (5m – 2p)(25m2 + 10mp + 4p2)

16)  (m2 – 2)(m4 + 2m2 + 4)

17)  (4y2 + 1)(16y4 – 4y2 + 1)

18)  (2k2 – 3q)(4k4 + 6k2q + 9q2)

19)  (5z + 4r2)(25z2 – 20r2z + 16r4)

20)  ((a – b) – (a + b))((a – b)2 + (a – b)(a + b) + (a + b)2)  =  -2b(3a2 + b2)