Question

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

Answer 1

Use the sum of cubes identity `a^3+b^3 = (a+b)(a^2-ab+b^2)` to find:

`x^3+8y^3 = (x+2y)(x^2-2xy+4y^2)`

Explanation:

Use the sum of cubes identity with `a = x` and `b = 2y`:

`x^3+8y^3 = x^3 + (2y)^3`

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

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