factoringggggg?

Question

1) y^3 - 64

2) y^3 - 64

3) b^3 + 8

4) 81y^2 - 121

oops. 1 & 2 are the same (:

Answer 1

y^3 - 64 = (y-4)(y^2 + 4y + 16)

b^3 + 8 = (y+2)(y^2 - 2y - 4)

81y^2 - 121 = (9y - 11)(9y + 11)

that's it! They all are patterns which need to be memorized. :)

Answer 2

Relevant formulas are:

Difference of cubes:
a^3 - b^3 = (a - b)(a² + ab + b²)

Sum of cubes:
a^3 + b^3 = (a + b)(a² - ab + b²)

Difference of squares:
a² - b² = (a + b)(a - b)

I'm assuming problem 1 or 2 must have been the sum of cubes, so they weren't the same:

PROBLEM 1:

y^3 - 64
= y^3 - 4^3

a = y
b = 4

= (y - 4)(y² + 4y + 16)

PROBLEM 2* (assuming it is a sum of cubes):

y^3 + 4^3

a = y
b = 4

= (y + 4)(y² - 4y + 16)

PROBLEM 3:

b^3 + 8
b^3 + 2^3

(b + 2)(b² + 2b + 4)

PROBLEM 4:

81y² - 121
(9y)² - 11²

= (9y + 11)(9y - 11)