Question

How do you factor `64x^3 - y^6`?

Answer 1

`64x^3-y^6=(4x-y^2)(16x^2+4xy^2+y^4)`

Explanation:

As `64x^3-y^6` can be written as `(4x)^3-(y^2)^3`, we can use the identity

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

Hence `64x^3-y^6=(4x)^3-(y^2)^3`

= `(4x-y^2)((4x)^2+4x×y^2+(y^2)^2)`

= `(4x-y^2)(16x^2+4xy^2+y^4)`