# How do you find the following product (4xy + y)^2?

Oct 24, 2016

$= 16 {x}^{2} {y}^{2} + 8 x {y}^{2} + {y}^{2}$

#### Explanation:

To expand the given squared sum polynomial we will apply this polynomial identity

$\textcolor{red}{{\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}}$

${\left(4 x y + y\right)}^{2}$
$= \textcolor{red}{{\left(4 x y\right)}^{2} + 2 \left(4 x y\right) y + {y}^{2}}$

$= 16 {x}^{2} {y}^{2} + 8 x {y}^{2} + {y}^{2}$