# How do you use the distributive property to simplify -(12-4x)+8(10-x)?

##### 1 Answer
Mar 24, 2018

The simplified form is $- 4 x + 68$

#### Explanation:

The Distributive Property is when you apply a coefficient to all terms inside a set of parentheses. For this expression, we will use The Distributive Property twice:

$- \left(12 - 4 x\right) + 8 \left(10 - x\right) = - 1 \times \left(12 - 4 x\right) + 8 \times \left(10 - x\right)$

Let's do the first distribution:

$- 1 \times \left(12 - 4 x\right) = \left(- 1 \times 12\right) - \left(- 1 \times 4 x\right) = \left(- 12\right) - \left(- 4 x\right)$

$\Rightarrow - 12 + 4 x$

...And now the second:

$8 \times \left(10 - x\right) = \left(8 \times 10\right) - \left(8 \times x\right) = \left(80\right) - \left(8 x\right)$

$\Rightarrow 80 - 8 x$

Finally, we put these two distributed expressions back into the original equation and simplify:

$- 12 + 4 x + 80 - 8 x = 4 x - 8 x + 80 - 12$

$\textcolor{red}{\Rightarrow - 4 x + 68}$