Factoring Sum and Difference of Cubes

Squares of a number

2

What is 8²?

64

3

12²

144

4

Solve 10² - 7².

51

5

The square of 7 plus the square of 6.

85

6

Solve 11² + 5².

146

Cubes of a number

2

What is 6³?

216

3

What is 9³?

729

4

The cube of 15?

3375

5

The cube of 3 + the cube of 5.

152

6

The cube of 4 times the cube of 2 divided by 8.

64

Cube root of a number

2

Cube root of 27

3

3

Cube root of 1000

10

4

Cube root of 8000

20

5

Cube root of 64 times cube root of 8 divided by 2³.

1

6

Cube root of 27 times cube root of 729. 

27

Factor Sum of cubes

2

What is the formula for the sum of two cubes 

a. (x-y)(x² -xy+y²)        b. (x+y)(x²+xy+y²) 

c. (x-y)(x² +xy+y²)       d. (x+y)(x² - xy+y²) 

D

3

Factor the sum of cubes x³+27

a. (x+3)(x²-3x+9)        b. (x-3)(x²-3x-9)

c. (x+3)(x²+3x-9)       d. (x+3)(x²+3x+9)

  A

4

Factor using sum of cubes 64+x³ 

a. (4+x)(16+4x+x)     b. (4+x)(20+x) 

c. (4+x)(16 - 4x+x²)    d. (4-x)(16+4x+x²)

C

5

Factor using sum of cubes 1000x³+ 729 

(10x+9)(100x² - 90x+81)

6

Factor 64x³+27y³

(4x+3y)(16x²-12xy+9y²)

Factor Difference of cubes

2

Factor x³-64 

a. (x-4)(x²-4x+16)          b. (x-4)(x²+4x+16) 

c. (x-4)(x²+4x-16)          d. (x-4)(x²+4x-16)

B

3

Factor 8x³-512 

a. (2x-8)(4x²+16x+64)        b. (2x-8)(4x²-16x-64)

 c. (2x-5)(2x²+12x-64)      d. (2x-4)(2x+4+10)

A

4

Factor 1000x³-1 

a. (10x+1)(10x-11x+1) 

b. (10x-1)(100x²+10x-1) 

c. (10x-1)(100x²-10x+1) 

d. (10x-1)(100x²+10x+1)

D

5

Factor 125x^3-8

(5x-2)(25x²+10x+4)

6

Factor 27x³-216 

(3x-6)(9x²+18x+36)