Factoring Sum of Cubes and Difference of Squares and Cubes

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)
• (2x + 1)(4x² - 2x + 1)
• (2x - 1)(4x² - 2x - 1)
• (2x + 1)(4x² +2x + 1)

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)
• (9x + 2)(3x² + 18x + 4)
• (3x²+4)(9x + 2)
• (27x + 8)(x² - 216x + 64)

Factor
27x³-64

• (3x-4)(9x²+12x+16)
• (3x-4)(9x²-12x+16)
• (3x+4)(9x²-12x+16)
• (3x+4)(9x²+12x+16)

Fully Factor the Following
216x³+125

• 6(x+5)³
• (6x+5)³
• (6x+5)(6x²-30x+25)
• (6x+5)(36x²-30x+25)

64-27a³

• (4-3a)(9a²+12a+16)

• (3a-4)(3a²+12a+16)

• (4-3a)(3a²+12a+16)

• (4-3a)³

Fully Factor the Following
8x³-27

• (2x+3)(4x²-6x+9)
• (2x-3)(4x²+6x+9)
• (2x-3)(4x²+6x-9)
• (2x-3)(2x²+6x+9)

Factor this difference of cubes:
x³ - 343

• (x + 7) (x² - 7x + 49)
• (x² + 1) (x - 343)
• (x - 7) (x² + 7x + 49)
• (x² - 343) (x + 1)

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

Factor:   x³ + 1

• (x + 1)³
• (x+1)(x² - x + 1)
• (x - 1) (x² + x - 1)
• (x + 1)(x² - 2x + 1)

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

• No

• Yes

• Yes, getting GCF first

• It is a sum of squares