# How do you expand: (4x + 5)^2?

Nov 14, 2017

See a solution process below;

#### Explanation:

The question is: What is ${\left(4 x + 5\right)}^{2}$

We can use this rule for quadratics:

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

Let $x = 4 x$ and let $y = 5$

Substituting gives:

${\left(\textcolor{red}{4 \times} + \textcolor{b l u e}{5}\right)}^{2} \implies$

${\textcolor{red}{\left(4 x\right)}}^{2} + \left(2 \cdot \textcolor{red}{4 x} \cdot \textcolor{b l u e}{5}\right) + {\textcolor{b l u e}{5}}^{2} \implies$

$16 {x}^{2} + 40 x + 25$