How do you factor the difference of two cubes x^3 - 216?

1 Answer
Apr 9, 2015

Remember this formula for factorizing difference of 2 cubes:
a^3−b^3=(a−b)(a^2+ab+b^2)

In x^3-216,

a^3=x^3
b^3=216

a= root3(x^3) = x
b=root3(216)= 6

Substitute a=x , b=6 into the formula of (a-b)(a^2+ab+b^2)

(x-6)(x^2 + (6xx) + 6^2) = (x-6)(x^2 + 6x+ 36)

(x-6)(x^2 + 6x+ 36) is the factorized form of x^3-216