Question

How do you factor the expression `27x^9 + 8y^6`?

Answer 1

`27x^9+8y^6=(3x^3+2y^2)(9x^6-6x^3y^2+4y^4)`

Explanation:

`27x^9+8y^6` is a binomial each of whose monomial is a cube. Hence we can use the identity

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

As such `27x^9+8y^6=(3x^3)^3+(2y^2)^3`

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

= `(3x^3+2y^2)(9x^6-6x^3y^2+4y^4)`