Factor the following:
125 w^3 - 8
125 w^3 - 8 = (5 w)^3 - 2^3:
(5 w)^3 - 2^3
Factor the difference of two cubes. (5 w)^3 - 2^3 = (5 w - 2) ((5 w)^2 + (5 w) 2 + 2^2):
(5 w - 2) ((5 w)^2 + 5 2 w + 2^2)
Multiply each exponent in 5 w by 2:
(5 w - 2) (5^2 w^2 + 5 2 w + 2^2)
5^2 = 25:
(5 w - 2) (25 w^2 + 5 2 w + 2^2)
5×2 = 10:
(5 w - 2) (25 w^2 + 10 w + 2^2)
2^2 = 4:
Answer: (5 w - 2) (25 w^2 + 10 w + 4)