How do you simplify the product (2x^2 + 5x - 3)(2x + 1)  and write it in standard form?

May 5, 2017

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{2 {x}^{2}} + \textcolor{red}{5 x} - \textcolor{red}{3}\right) \left(\textcolor{b l u e}{2 x} + \textcolor{b l u e}{1}\right)$ becomes:

$\left(\textcolor{red}{2 {x}^{2}} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{2 {x}^{2}} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{1}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{2 x}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{1}\right)$

$4 {x}^{3} + 2 {x}^{2} + 10 {x}^{2} + 5 x - 6 x - 3$

We can now combine like terms:

$4 {x}^{3} + \left(2 + 10\right) {x}^{2} + \left(5 - 6\right) x - 3$

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

$4 {x}^{3} + 12 {x}^{2} - 1 x - 3$

$4 {x}^{3} + 12 {x}^{2} - x - 3$