Sum and Difference of Cubes

Question 1

Factor completely: x^3 - 1.

Accepted Answer

(x - 1)(x^2 + x + 1)

Answer

(x - 1)(x^2 - x + 1)

Answer

(x + 1)(x^2 - x + 1)

Answer

(x - 1)(x^2 + 2x + 1)

Question 2

Factor completely: 4x^4 + 256x.

Accepted Answer

4x(x + 4)(x^2 - 4x + 16)

Answer

4x(x + 4)(x^2 + 4x + 16)

Answer

4x(x - 4)(x^2 + 4x + 16)

Answer

4x(x^3 + 64)

Question 3

Factor completely: 2x^4 - 2x.

Accepted Answer

2x(x - 1)(x^2 + x + 1)

Answer

2x(x - 1)(x^2 - x + 1)

Answer

2x(x + 1)(x^2 - x + 1)

Answer

2x(x^3 - 1)

Question 4

Factor completely: x^3 + 216.

Accepted Answer

(x + 6)(x^2 - 6x + 36)

Answer

(x + 6)(x^2 + 6x + 36)

Answer

(x - 6)(x^2 + 6x + 36)

Answer

(x + 6)(x^2 - 12x + 36)

Question 5

Factor completely: 4x^4 - 4x.

Accepted Answer

4x(x - 1)(x^2 + x + 1)

Answer

4x(x - 1)(x^2 - x + 1)

Answer

4x(x + 1)(x^2 - x + 1)

Answer

4x(x^3 - 1)

Question 6

Factor completely: 125x^3 - 27.

Accepted Answer

(5x - 3)(25x^2 + 15x + 9)

Answer

(5x - 3)(25x^2 - 15x + 9)

Answer

(5x + 3)(25x^2 - 15x + 9)

Answer

(5x - 3)(25x^2 + 30x + 9)

Question 7

Factor 8x^6 - 8 as a difference of cubes, using a = 2x^2 and b = 2.

Accepted Answer

(2x^2 - 2)(4x^4 + 4x^2 + 4)

Answer

(2x^2 - 2)(4x^4 - 4x^2 + 4)

Answer

(2x^2 + 2)(4x^4 - 4x^2 + 4)

Answer

(2x^2 - 2)(4x^4 + 8x^2 + 4)

Question 8

Factor completely: 125x^3 + 64.

Accepted Answer

(5x + 4)(25x^2 - 20x + 16)

Answer

(5x + 4)(25x^2 + 20x + 16)

Answer

(5x - 4)(25x^2 + 20x + 16)

Answer

(5x + 4)(25x^2 - 40x + 16)

Question 9

A student factors 8x^3 - 8 as (2x - 2)(4x^2 - 4x + 4), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

8(x - 1)(x^2 + x + 1)

Answer

8(x - 1)(x^2 - x + 1)

Answer

8(x + 1)(x^2 - x + 1)

Answer

(2x - 2)(4x^2 + 4x + 4)

Question 10

Factor completely: 64x^3 - 216.

Accepted Answer

8(2x - 3)(4x^2 + 6x + 9)

Answer

8(2x - 3)(4x^2 - 6x + 9)

Answer

8(2x + 3)(4x^2 - 6x + 9)

Answer

(4x - 6)(16x^2 + 24x + 36)

Question 11

Factor completely: 8x^3 + 64.

Accepted Answer

8(x + 2)(x^2 - 2x + 4)

Answer

8(x + 2)(x^2 + 2x + 4)

Answer

8(x - 2)(x^2 + 2x + 4)

Answer

(2x + 4)(4x^2 - 8x + 16)

Question 12

A student factors x^3 - 8 as (x - 2)(x^2 - 2x + 4), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x - 2)(x^2 - 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)(x^2 + 4x + 4)

Question 13

Factor completely: 64x^3 - 125.

Accepted Answer

(4x - 5)(16x^2 + 20x + 25)

Answer

(4x - 5)(16x^2 - 20x + 25)

Answer

(4x + 5)(16x^2 - 20x + 25)

Answer

(4x - 5)(16x^2 + 40x + 25)

Question 14

Factor completely: x^3 + 8.

Accepted Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x + 2)(x^2 + 2x + 4)

Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 4x + 4)

Question 15

Factor completely: 125x^3 - 8.

Accepted Answer

(5x - 2)(25x^2 + 10x + 4)

Answer

(5x - 2)(25x^2 - 10x + 4)

Answer

(5x + 2)(25x^2 - 10x + 4)

Answer

(5x - 2)(25x^2 + 20x + 4)

Question 16

Factor completely: 2x^4 - 128x.

Accepted Answer

2x(x - 4)(x^2 + 4x + 16)

Answer

2x(x - 4)(x^2 - 4x + 16)

Answer

2x(x + 4)(x^2 - 4x + 16)

Answer

2x(x^3 - 64)

Question 17

A student factors 125x^3 - 27 as (5x - 3)(25x^2 - 15x + 9), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(5x - 3)(25x^2 + 15x + 9)

Answer

(5x - 3)(25x^2 - 15x + 9)

Answer

(5x + 3)(25x^2 - 15x + 9)

Answer

(5x - 3)(25x^2 + 30x + 9)

Question 18

Factor completely: 8x^3 - 1.

Accepted Answer

(2x - 1)(4x^2 + 2x + 1)

Answer

(2x - 1)(4x^2 - 2x + 1)

Answer

(2x + 1)(4x^2 - 2x + 1)

Answer

(2x - 1)(4x^2 + 4x + 1)

Question 19

Factor completely: 3x^4 - 81x.

Accepted Answer

3x(x - 3)(x^2 + 3x + 9)

Answer

3x(x - 3)(x^2 - 3x + 9)

Answer

3x(x + 3)(x^2 - 3x + 9)

Answer

3x(x^3 - 27)

Question 20

Factor completely: 27x^6 - 1.

Accepted Answer

(3x^2 - 1)(9x^4 + 3x^2 + 1)

Answer

(3x^2 - 1)(9x^4 - 3x^2 + 1)

Answer

(3x^2 + 1)(9x^4 - 3x^2 + 1)

Answer

(3x^2 - 1)(9x^4 + 6x^2 + 1)

Question 21

Factor completely: x^3 - 125.

Accepted Answer

(x - 5)(x^2 + 5x + 25)

Answer

(x - 5)(x^2 - 5x + 25)

Answer

(x + 5)(x^2 - 5x + 25)

Answer

(x - 5)(x^2 + 10x + 25)

Question 22

Factor completely: 3x^4 - 192x.

Accepted Answer

3x(x - 4)(x^2 + 4x + 16)

Answer

3x(x - 4)(x^2 - 4x + 16)

Answer

3x(x + 4)(x^2 - 4x + 16)

Answer

3x(x^3 - 64)

Question 23

A student factors x^3 - 216 as (x - 6)(x^2 - 6x + 36), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(x - 6)(x^2 + 6x + 36)

Answer

(x - 6)(x^2 - 6x + 36)

Answer

(x + 6)(x^2 - 6x + 36)

Answer

(x - 6)(x^2 + 12x + 36)

Question 24

Factor completely: 8x^3 + 216.

Accepted Answer

8(x + 3)(x^2 - 3x + 9)

Answer

8(x + 3)(x^2 + 3x + 9)

Answer

8(x - 3)(x^2 + 3x + 9)

Answer

(2x + 6)(4x^2 - 12x + 36)

Question 25

Factor completely: x^6 + 1.

Accepted Answer

(x^2 + 1)(x^4 - x^2 + 1)

Answer

(x^2 + 1)(x^4 + x^2 + 1)

Answer

(x^2 - 1)(x^4 + x^2 + 1)

Answer

(2x^2 + 1)(x^4 - x^2 + 1)

Question 26

A student factors 64x^3 - 27 as (4x - 3)(16x^2 - 12x + 9), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(4x - 3)(16x^2 + 12x + 9)

Answer

(4x - 3)(16x^2 - 12x + 9)

Answer

(4x + 3)(16x^2 - 12x + 9)

Answer

(4x - 3)(16x^2 + 24x + 9)

Question 27

Factor completely: x^3 - 27.

Accepted Answer

(x - 3)(x^2 + 3x + 9)

Answer

(x - 3)(x^2 - 3x + 9)

Answer

(x + 3)(x^2 - 3x + 9)

Answer

(x - 3)(x^2 + 6x + 9)

Question 28

A student factors x^3 - 125 as (x - 5)(x^2 - 5x + 25), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(x - 5)(x^2 + 5x + 25)

Answer

(x - 5)(x^2 - 5x + 25)

Answer

(x + 5)(x^2 - 5x + 25)

Answer

(x - 5)(x^2 + 10x + 25)

Question 29

Factor completely: 125x^3 + 216.

Accepted Answer

(5x + 6)(25x^2 - 30x + 36)

Answer

(5x + 6)(25x^2 + 30x + 36)

Answer

(5x - 6)(25x^2 + 30x + 36)

Answer

(5x + 6)(25x^2 - 60x + 36)

Question 30

Factor completely: 8x^3 + 8.

Accepted Answer

8(x + 1)(x^2 - x + 1)

Answer

8(x + 1)(x^2 + x + 1)

Answer

8(x - 1)(x^2 + x + 1)

Answer

8(x + 1)(x^2 - 2x + 1)

Question 31

Factor completely: 64x^6 + 8.

Accepted Answer

8(2x^2 + 1)(4x^4 - 2x^2 + 1)

Answer

8(2x^2 + 1)(4x^4 + 2x^2 + 1)

Answer

8(2x^2 - 1)(4x^4 + 2x^2 + 1)

Answer

8(2x^2 + 1)(4x^4 - 4x^2 + 1)

Question 32

Factor completely: 64x^6 + 1.

Accepted Answer

(4x^2 + 1)(16x^4 - 4x^2 + 1)

Answer

(4x^2 + 1)(16x^4 + 4x^2 + 1)

Answer

(4x^2 - 1)(16x^4 + 4x^2 + 1)

Answer

(8x^2 + 1)(16x^4 - 4x^2 + 1)

Question 33

Factor completely: 125x^3 + 125.

Accepted Answer

125(x + 1)(x^2 - x + 1)

Answer

125(x + 1)(x^2 + x + 1)

Answer

125(x - 1)(x^2 + x + 1)

Answer

125(x + 1)(x^2 - 2x + 1)

Question 34

Factor completely: 5x^4 - 320x.

Accepted Answer

5x(x - 4)(x^2 + 4x + 16)

Answer

5x(x - 4)(x^2 - 4x + 16)

Answer

5x(x + 4)(x^2 - 4x + 16)

Answer

5x(x^3 - 64)

Question 35

Factor completely: 3x^4 - 3x.

Accepted Answer

3x(x - 1)(x^2 + x + 1)

Answer

3x(x - 1)(x^2 - x + 1)

Answer

3x(x + 1)(x^2 - x + 1)

Answer

3x(x^3 - 1)

Question 36

Factor completely: 27x^6 + 8.

Accepted Answer

(3x^2 + 2)(9x^4 - 6x^2 + 4)

Answer

(3x^2 + 2)(9x^4 + 6x^2 + 4)

Answer

(3x^2 - 2)(9x^4 + 6x^2 + 4)

Answer

(3x^2 + 2)(9x^4 - 12x^2 + 4)

Question 37

A student factors 125x^3 - 125 as (5x - 5)(25x^2 - 25x + 25), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

125(x - 1)(x^2 + x + 1)

Answer

125(x - 1)(x^2 - x + 1)

Answer

125(x + 1)(x^2 - x + 1)

Answer

125(x - 1)(x^2 + 2x + 1)

Question 38

Factor completely: 4x^4 + 108x.

Accepted Answer

4x(x + 3)(x^2 - 3x + 9)

Answer

4x(x + 3)(x^2 + 3x + 9)

Answer

4x(x - 3)(x^2 + 3x + 9)

Answer

4x(x^3 + 27)

Question 39

Factor completely: 3x^4 + 24x.

Accepted Answer

3x(x + 2)(x^2 - 2x + 4)

Answer

3x(x + 2)(x^2 + 2x + 4)

Answer

3x(x - 2)(x^2 + 2x + 4)

Answer

3x(x^3 + 8)

Question 40

A student factors 125x^3 - 1 as (5x - 1)(25x^2 - 5x + 1), copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Accepted Answer

(5x - 1)(25x^2 + 5x + 1)

Answer

(5x - 1)(25x^2 - 5x + 1)

Answer

(5x + 1)(25x^2 - 5x + 1)

Answer

(5x - 1)(25x^2 + 10x + 1)

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Sum and Difference of Cubes

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Sum and Difference of Cubes

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner