# How do you find the product of (-9x^2-10y)^2?

Jul 8, 2016

${\left(- 9 {x}^{2} - 10 y\right)}^{2} = \textcolor{b l u e}{81 {x}^{4} + 180 {x}^{2} y + 100 {y}^{2}}$

#### Explanation:

In general ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

If $a = - 9 {x}^{2}$ and $b = - 10 y$
then
$\textcolor{w h i t e}{\text{XXX")a^2color(white)("XXX}} = 81 {x}^{4}$
$\textcolor{w h i t e}{\text{XXX")2abcolor(white)("XX}} = 180 {x}^{2} y$
$\textcolor{w h i t e}{\text{XXX")b^2color(white)("XXX}} = \underline{100 {y}^{2}}$
$\textcolor{w h i t e}{\text{XXXXXXXXXX}} 81 {x}^{4} + 180 {x}^{2} y + 100 {y}^{2}$