Question

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

Answer 1

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.