# How do you use the distributive property to simplify (4)(2x - 5) - 2(3x^2 - 2)?

Jun 11, 2018

$- 6 {x}^{2} + 8 x - 16$

#### Explanation:

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

To simplify this, we use the distributive property (shown below):
$h \texttt{p} : / c \mathrm{dn} . v i r t u a \ln e r d . c o \frac{m}{t} h u m b n a i l \frac{s}{A} l g {1}_{1} l - \mathrm{di} a g r a {m}_{t} h u m b - l g p n g$

Following this image, we know that:
$\textcolor{b l u e}{4 \left(2 x - 5\right) = \left(4 \cdot 2 x\right) + \left(4 \cdot - 5\right) = 8 x - 20}$
and
$\textcolor{b l u e}{- 2 \left(3 {x}^{2} - 2\right) = \left(- 2 \cdot 3 {x}^{2}\right) + \left(- 2 \cdot - 2\right) = - 6 {x}^{2} + 4}$

Combine them:
$8 x - 20 - 6 {x}^{2} + 4$

Combine the like terms $\textcolor{b l u e}{- 20}$ and $\textcolor{b l u e}{4}$:
$8 x - 16 - 6 {x}^{2}$

Since we typically write it when the highest exponent degree first, it becomes:
$- 6 {x}^{2} + 8 x - 16$

Hope this helps!

Jun 11, 2018

$\left(4\right) \left(2 x - 5\right) - 2 \left(3 {x}^{2} - 2\right) = - 6 {x}^{2} + 8 x - 16$

#### Explanation:

The distributive law is applied to multiply a monomial factor into a bracket.

The number outside is multiplied by each term inside the bracket:

$\textcolor{red}{a} \left(\textcolor{b l u e}{b + c + d}\right) = \textcolor{red}{a} \textcolor{b l u e}{b} + \textcolor{red}{a} \textcolor{b l u e}{c} + \textcolor{red}{a} \textcolor{b l u e}{d}$

$\text{ } \textcolor{red}{\left(4\right)} \left(\textcolor{b l u e}{2 x - 5}\right) - \textcolor{g r e e n}{\left(2\right)} \left(\textcolor{p u r p \le}{3 {x}^{2} - 2}\right)$

$= \textcolor{red}{4} \textcolor{b l u e}{\left(2 x\right)} + \textcolor{red}{4} \textcolor{b l u e}{\left(- 5\right)} - \textcolor{g r e e n}{2} \textcolor{p u r p \le}{\left(3 {x}^{2}\right)} - \textcolor{g r e e n}{2} \textcolor{p u r p \le}{\left(- 2\right)}$
$\textcolor{w h i t e}{\times \times} \downarrow \textcolor{w h i t e}{\times \times} \downarrow \textcolor{w h i t e}{\times \times} \downarrow \textcolor{w h i t e}{\times \times} \downarrow$
$= \text{ "8x" "-20" " -6x^2" "+4" } \leftarrow$ collect like terms

$= - 6 {x}^{2} + 8 x - 16$