# How do you find the product (2/5y-4)^2?

Jun 16, 2017

$\left(\frac{2}{5} y - 4\right) = \textcolor{m a \ge n t a}{\frac{4}{25} {y}^{2} - \frac{8}{5} y + 16}$

#### Explanation:

Use the general relation ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$
with $a = \frac{2}{5} y$ and $b = 4$

or work it through in detail using the distributive property:
${\left(\frac{2}{5} y - 4\right)}^{2}$
$\textcolor{w h i t e}{\text{XXX")=color(red)(""(2/5y-4))xxcolor(blue)(} \left(\frac{2}{5} y - 4\right)}$

$\textcolor{w h i t e}{\text{XXX")=color(red)(2/5y)xxcolor(blue)(""(2/5y-4))color(red)(-4)xxcolor(blue)(} \left(\frac{2}{5} y - 4\right)}$

color(white)("XXX")=(color(red)(2/5y)xxcolor(blue)(2/5y)-color(red)(2/5y)xxcolor(blue)4)-(color(red)4xxcolor(blue)(2/5y)-color(red)4xxcolor(blue)(""(-4)))

$\textcolor{w h i t e}{\text{XXX}} = \left(\frac{4}{25} {y}^{2} - \frac{8}{5} y\right) - \left(\frac{8}{5} y - 16\right)$

$\textcolor{w h i t e}{\text{XXX}} = \frac{4}{25} {y}^{2} - \frac{16}{5} y + 16$