How do you multiply (5x^2-5y)^2?

Feb 13, 2017

See the entire solution process below:

Explanation:

This expression can be rewritten as:

(5x^2 - 5y)(5x^2 - 5y)

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

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

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

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

We can now combine like terms:

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

$25 {x}^{4} - 50 {x}^{2} y + 25 {y}^{2}$

If necessary, we can factor out a $25$ from each term to give:

25(x^4 - 2x^2y + y^2)