Question

How do you use the difference of two cubes formula to factor `x^6-y^3`?

Answer 1

`x^6 - y^3 = (x^2)^3 - y^3`

The Difference of Cubes Formula says

`color(blue)(a^3 - b^3 = (a-b)(a^2 +ab+b^2)`

Hence `(x^2)^3 - y^3 = (x^2 - y)((x^2)^2 +x^2y +y^2)`

`=color(green)( (x^2 - y)(x^4 +x^2y + y^2)`