# How do you simplify (5-2x)^2?

Jun 14, 2018

See a solution process below:

#### Explanation:

For this special case of quadratics we can use this rule to expand and simplify this expression:

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

Substituting the values from the problem gives:

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

$\left(\textcolor{red}{5} - \textcolor{b l u e}{2 x}\right) \left(\textcolor{red}{5} - \textcolor{b l u e}{2 x}\right) \implies$

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

$25 - 20 x + 4 {x}^{2}$

Or, in standard form:

$4 {x}^{2} - 20 x + 25$