How do you simplify -4x^3(2x^4-5y)?

1 Answer
Dec 22, 2016

color(magenta)(-8x^7+20x^3y

Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{- 4 {x}^{3}} \left(\textcolor{b l u e}{2 {x}^{4}} - \textcolor{g r e e n}{5 y}\right)$

Using the Distributive Property this becomes
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{red}{- 4 {x}^{3}}\right) \cdot \left(\textcolor{b l u e}{2 {x}^{4}}\right) - \left(\textcolor{red}{- 4 {x}^{3}}\right) \cdot \left(\textcolor{g r e e n}{5 y}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left(\textcolor{red}{- 4}\right) \cdot \textcolor{b l u e}{2} \cdot \textcolor{red}{{x}^{3}} \cdot \textcolor{b l u e}{{x}^{4}} - \left(\textcolor{red}{- 4}\right) \cdot \textcolor{g r e e n}{5} \cdot \textcolor{red}{{x}^{3}} \cdot \textcolor{g r e e n}{y}$

$\textcolor{w h i t e}{\text{XXX}} = - 8 {x}^{7} - \left(- 20 {x}^{3} y\right)$

$\textcolor{w h i t e}{\text{XXX}} = - 8 {x}^{7} + 20 {x}^{3} y$