How do you factor x^3-8y^3?

1 Answer
Apr 9, 2015

We can write this expression as x^3-(2y)^3

The formula for factorizing the Difference of two Cubes is:
a^3−b^3=(a−b)(a^2+ab+b^2)

In x^3-(2y)^3,
a=x
b=2y

x^3-(2y)^3
= (x-2y)*(x^2+(x*2y)+(2y)^2)
= color(green)( (x-2y)*(x^2+2xy+4y^2)

As we cannot factorize any of the factors further, we can say that we have factorised x^3-8y^3 completely.