# How do you multiply (2x - 3)(x^2 + 5^x - 3)?

Sep 15, 2015

$2 {x}^{3} - 3 {x}^{2} + \left(2 x - 3\right) {5}^{x} - 6 x + 9$
$\textcolor{w h i t e}{\text{XXXX}}$(although one has to wonder if ${5}^{x}$ wasn't meant to be $5 x$)

#### Explanation:

$\left(\textcolor{red}{2 x} - \textcolor{b l u e}{3}\right) \left({x}^{2} + {5}^{x} - 3\right)$

$= \textcolor{red}{2 x} \left({x}^{2} + {5}^{x} - 3\right) - \textcolor{b l u e}{3} \left({x}^{2} + {5}^{x} - 3\right)$

$= \left(\textcolor{red}{2 {x}^{3} + 2 x \cdot {5}^{x} - 6 x}\right) - \left(\textcolor{b l u e}{3 {x}^{2} + 3 \cdot {5}^{x} - 9}\right)$

$= 2 {x}^{3} - 3 {x}^{2} + \left(2 x - 3\right) {5}^{x} - 6 x + 9$