Question

How do you factor `x^6 + 2x^3y^2 + y^4`?

Answer 1

`x^6+2x^3y^2+y^4 = (x^3+y^2)^2`

Explanation:

We can recognise this as a perfect square trinomial, since it is of the form `a^2+2ab+b^2` with `a=x^3` and `b=y^2`.

`x^6+2x^3y^2+y^4`

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

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