How do you use the distributive property to simplify –9 + 4(2x – 1) + 8?

May 27, 2018

$8 x - 5$

Explanation:

$- 9 + 4 \left(2 x - 1\right) + 8$

First, we know that $- 9 + 8$ simplifies to $- 1$, so it becomes;
$- 1 + 4 \left(2 x - 1\right)$

Now we use the distributive property (shown below) to simplify/expand $4 \left(2 x - 1\right)$:

Following this image, we know that:
$\textcolor{b l u e}{4 \left(2 x - 1\right) = \left(4 \cdot 2 x\right) + \left(4 \cdot - 1\right) = 8 x - 4}$

Put that back into the expression:
$- 1 + 8 x - 4$

Simplify $- 1 - 4 = - 5$:
Therefore, the simplified expression is:
$- 5 + 8 x$

We typically put variables before pure numbers, so the expression becomes:
$8 x - 5$

Hope this helps!