# How do you simplify the product (2x - 5)(x + 4) and write it in standard form?

Mar 31, 2017

$2 {x}^{2} + 3 x - 20$

#### Explanation:

$\left(2 x - 5\right) \left(x + 4\right)$

$2 x \times x = 2 {x}^{2}$

$2 x \times 4 = 8 x$

$- 5 \times x = - 5 x$

$- 5 \times 4 = - 20$

$8 x - 5 x = 3 x$

The answer is $2 {x}^{2} + 3 x - 20$

Mar 31, 2017

$\left(2 x - 5\right) \left(x + 4\right) = \textcolor{b l u e}{2 {x}^{2} + 3 x - 20}$

#### Explanation:

Expand:

$\left(2 x - 5\right) \left(x + 4\right)$

When multiplying two binomials, use the FOIL method as shown below. Then combine like terms and simplify, which will result in the standard form for a quadratic equation, $a {x}^{2} + b x + c$. $\left(2 x - 5\right) \left(x + 4\right)$, where $a x = 2 x$, $b = - 5$, $c x = x$, $d = 4$.

Carry out the FOIL method for two multiplying binomials.

$\left(2 x - 5\right) \left(x + 4\right) = 2 x \cdot x + 2 x \cdot 4 + \left(- 5\right) \cdot x + \left(- 5 \cdot 4\right)$

$\left(2 x - 5\right) \left(x + 4\right) = 2 {x}^{2} + 8 x - 5 x - 20$

Combine like terms.

$\left(2 x - 5\right) \left(x + 4\right) = 2 {x}^{2} + 8 x - 5 x - 20$

Simplify.

$\left(2 x - 5\right) \left(x + 4\right) = \textcolor{b l u e}{2 {x}^{2} + 3 x - 20}$$\Leftarrow$ standard form