# How do you factor completely 48x^2 + 48xy^2 + 12y^4?

##### 1 Answer
Jan 6, 2016

$12 {\left(2 x + {y}^{2}\right)}^{2}$

#### Explanation:

Step one: Factor out the greatest common factor (which is 12):
$12 \left(4 {x}^{2} + 4 x {y}^{2} + {y}^{4}\right)$

Step two: Recognize that this is a perfect square. Remember that Perfect Square Trinomials have:
a) first and last terms that are positive perfect squares (in this case, $4 {x}^{2}$ and ${y}^{4}$.
AND
b) the middle term is twice the product of the square roots of the first and third terms (in this case $2 x {y}^{2} \times 2 = 4 x {y}^{2}$

When you have a perfect square, you can factor it by taking the square root of the first and last terms, putting them inside a bracket, and squaring the bracket:

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

Step three: Putting the 12 in front (that you factored out in the first step) completes the answer:
$12 {\left(2 x + {y}^{2}\right)}^{2}$