Question

How do you factor `8x^3 - y^6`?

Answer 1

`8x^3 - y^6 = (2x)^3 - (y^2)^3`

We can use the Identity `color(blue)(a^3 - b^3 = (a - b)(a^2 +ab+b^2)`

We get `(2x - y^2){(2x)^2 +(2x)(y^2)+(y^2)^2}`

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

As none of the factors above can be factorised further, it is the factorised form of `8x^3 - y^6`