# How do you multiply (2x^2-5x-1)(x^2+x-3)?

Aug 5, 2015

$\left(2 {x}^{2} - 5 x - 1\right) \left({x}^{2} + x - 3\right) = 2 {x}^{4} - 8 {x}^{3} - 12 {x}^{2} + 14 x + 3$

#### Explanation:

$\left(p\right) \cdot \left({x}^{2} + x - 3\right) = \left(p {x}^{2} + p x - 3 p\right)$

Replacing $\left(p\right)$ with $\left(2 {x}^{2} - 5 x - 1\right)$

$\left(2 {x}^{2} - 5 x - 1\right) \left({x}^{2} + x - 3\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(2 {x}^{2} - 5 x - 1\right) {x}^{2} + \left(2 {x}^{2} - 5 x - 1\right) x - 3 \left(2 {x}^{2} - 5 x - 1\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(2 {x}^{4} - 10 {x}^{3} - {x}^{2}\right) + \left(2 {x}^{3} - 5 {x}^{2} - x\right) - \left(6 {x}^{2} - 15 x - 3\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(2 {x}^{4}\right) + \left(- 10 {x}^{3} + 2 {x}^{3}\right) + \left(- {x}^{2} - 5 {x}^{2} - 6 {x}^{2}\right) + \left(- x + 15 x\right) + \left(3\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= 2 {x}^{4} - 8 {x}^{3} - 12 {x}^{2} + 14 x + 3$