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

Jun 17, 2017

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

#### Explanation:

To solve this problem first you rewrite as follows:

$\left(\textcolor{b l u e}{5 x} \textcolor{\mathrm{da} r k red}{- 2}\right) \left(\textcolor{red}{5 x} \textcolor{g r e e n}{- 2}\right)$

Then you proceed to FOIL it:

Where you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\left(\textcolor{b l u e}{5 x}\right) \left(\textcolor{red}{5 x}\right) = 25 {x}^{2}$

$\left(\textcolor{b l u e}{5 x}\right) \left(\textcolor{g r e e n}{- 2}\right) = - 10 x$

Now you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\textcolor{\mathrm{da} r k red}{\left(- 2\right)} \left(\textcolor{red}{5 x}\right) = - 10 x$

$\textcolor{\mathrm{da} r k red}{\left(- 2\right)} \left(\textcolor{g r e e n}{- 2}\right) = 4$

Now combine them:

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

Simplify:

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

Jun 17, 2017

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

#### Explanation:

$\text{express " (5x-2)^2" as } \left(5 x - 2\right) \left(5 x - 2\right)$

$\text{each term in the second bracket is multiplied by each term in}$
$\text{the first bracket}$

$\left(\textcolor{red}{5 x - 2}\right) \left(5 x - 2\right)$

$= \textcolor{red}{5 x} \left(5 x - 2\right) \textcolor{red}{- 2} \left(5 x - 2\right)$

$= \left(\textcolor{red}{5 x} \times 5 x\right) + \left(\textcolor{red}{5 x} \times - 2\right) + \left(\textcolor{red}{- 2} \times 5 x\right) + \left(\textcolor{red}{- 2} \times - 2\right)$

$= 25 {x}^{2} + \left(- 10 x\right) + \left(- 10 x\right) + 4$

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

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