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

Question

1705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-18T06:36:19

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

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

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

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

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

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

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