Question

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

Answer 1

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

Explanation:

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

Think about Pascal's Triangle to expand these terms:
`= (x^3 + 3xy^2 + 3x^2y + y^3) + (x^3 + 3xy^2 - 3x^2y - y^3)`

Combine like terms
`= 2x^3 + 6xy^2`

Factor:
`= (2x)(x^2+3y^2)`

Answer 2

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

Explanation:

`"this is a "color(blue)"sum of cubes"`

`•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)`

`"here "a=x+y" and "b=x-y`

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

`=2x[x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2]`

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