# What is the standard form of a polynomial (2x – 6)^2?

May 28, 2018

See a solution process below:

#### Explanation:

We can use this special rule for quadratics to put this expression in standard form.

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

Substituting the values from the problem gives:

${\left(\textcolor{red}{2 x} - \textcolor{b l u e}{6}\right)}^{2} \implies \left(\textcolor{red}{2 x} - \textcolor{b l u e}{6}\right) \left(\textcolor{red}{2 x} - \textcolor{b l u e}{6}\right) \implies {\left(\textcolor{red}{2 x}\right)}^{2} - \left(2 \cdot \textcolor{red}{2 x} \cdot \textcolor{b l u e}{6}\right) + {\textcolor{b l u e}{6}}^{2} \implies$

$4 {x}^{2} - 24 x + 36$