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

Jan 3, 2016

${x}^{6} + 2 {x}^{3} {y}^{2} + {y}^{4} = {\left({x}^{3} + {y}^{2}\right)}^{2}$

#### Explanation:

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

${x}^{6} + 2 {x}^{3} {y}^{2} + {y}^{4}$

$= {\left({x}^{3}\right)}^{2} + 2 \left({x}^{3}\right) \left({y}^{2}\right) + {\left({y}^{2}\right)}^{2}$

$= {\left({x}^{3} + {y}^{2}\right)}^{2}$