Factoring Perfect Squares and Cubes

Complete the formula (use your notes!)
a³-b³=

• (a-b)(a²+ab+b²)
• (a+b)(a²-ab+b²)
• (a-b)(a²-ab+b²)
• (a+b)(a²+ab+b²)

Factor:
x³ + 27

• (x + 3) (x² - 3x + 9)
• (x - 3) (x² + 3x + 9)
• (x + 3)(x + 9)
• Prime
  (can't be factored)

Factor. 
x³ + 125

• (x + 5)(x² - 5x + 25)
• (x + 5)(x - 5)
• (x - 5)(x² + 5x + 1)
• prime

Factor.

27 - x³

• (3 - x)(9 + 3x + 9)

• (3 + x)(3 - x)

• (3 - x)(9 + 3x + x²)

• prime

Factor. 
8x³ + 1

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

Factor:   x³ + 1

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

Factor:  27x³ + 8

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

Fully Factor the Following
216x³+125

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

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

64-27a³

• (4-3a)(16 + 12a + 9a²)

• (3a-4)(3a²+12a-16)

• (4-3a)(3a²-12a+16)

• (4-3a)³