# How do you multiply (-20x -12)(-19x -15)?

May 9, 2018

$380 {x}^{2} + 528 x + 180$

#### Explanation:

$\textcolor{red}{\left(- 20 x - 12\right) \left(- 19 x - 15\right)}$

doing this is like doing $2 \left(x + 4\right)$
you times the number outside the brackets, $\textcolor{b l u e}{2}$, with everything inside the brackets, $\textcolor{b l u e}{\left(x + 4\right)}$
2 xx x = color(blue)(2x
$2 \times 4 = \textcolor{b l u e}{8}$
$\textcolor{b l u e}{2 x + 8}$
$2 \left(x + 4\right)$ becomes $2 x + 8$

So, with $\textcolor{red}{\left(- 20 x - 12\right) \left(- 19 x - 15\right)}$
You times these together first...
$\left(\textcolor{red}{- 20 x} - 12\right) \left(\textcolor{red}{- 19 x - 15}\right)$
like...
-20x xx -19x = color(blue)(380x^2
-20x xx -15 = color(blue)(300x

then you do the same with...
$\left(- 20 x \textcolor{red}{- 12}\right) \left(\textcolor{red}{- 19 x - 15}\right)$
like...
-12 xx -19x = color(blue)(228x
$- 12 \times - 15 = \textcolor{b l u e}{180}$

When you put everything together, you get something like this
color(blue)(380x^2 + 300x + 228x + 180
And when you solve that...

$380 {x}^{2} \textcolor{b l u e}{+ 300 x + 228 x} + 180$
$380 {x}^{2} \textcolor{b l u e}{+ 528 x} + 180$