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

Jun 25, 2015

 = color(blue)(2x^3 + 5x^2 -7x -15

#### Explanation:

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

• Here, we first multiply $\textcolor{b l u e}{2 x}$contained in the first bracket with all three terms of second bracket:

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

$= 2 {x}^{3} + 2 {x}^{2} - 10 x$........................$\left(1\right)$

• Now, we multiply $\textcolor{b l u e}{3}$ contained in the first bracket with all three terms of second bracket:

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

$= 3 {x}^{2} + 3 x - 15$.........................$\left(2\right)$

combining $\left(1\right)$ and $\left(2\right)$

 = color(blue)(2x^3 + 5x^2 -7x -15