Question

How do you factor `x^3 + (x + y)^3`?

Answer 1

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

Explanation:

Here, we can use the identity `a^3+b^3=(a+b)(a^2-ab+b^2)`

Hence `x^3+(x+y)^3`

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

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

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