# How do you find the product (5x^2-y^2)^2?

Feb 1, 2017

See the entire solution process below:

#### Explanation:

First, we can rewrite this expression as:

$\left(5 {x}^{2} - {y}^{2}\right) \left(5 {x}^{2} - {y}^{2}\right)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{5 {x}^{2}} - \textcolor{red}{{y}^{2}}\right) \left(\textcolor{b l u e}{5 {x}^{2}} - \textcolor{b l u e}{{y}^{2}}\right)$ becomes:

$\left(\textcolor{red}{5 {x}^{2}} \times \textcolor{b l u e}{5 {x}^{2}}\right) - \left(\textcolor{red}{5 {x}^{2}} \times \textcolor{b l u e}{{y}^{2}}\right) - \left(\textcolor{red}{{y}^{2}} \times \textcolor{b l u e}{5 {x}^{2}}\right) + \left(\textcolor{red}{{y}^{2}} \times \textcolor{b l u e}{{y}^{2}}\right)$

$25 {x}^{4} - 5 {x}^{2} {y}^{2} - 5 {x}^{2} {y}^{2} + {y}^{4}$

We can now combine like terms:

$25 {x}^{4} + \left(- 5 - 5\right) {x}^{2} {y}^{2} + {y}^{4}$

$25 {x}^{4} - 10 {x}^{2} {y}^{2} + {y}^{4}$