Question

Use the Distributive Property to rewrite each expression. Then simplify.

$\mathbf{2}\mathbf{(}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{4}\mathbf{)}$

Short answer

The simplified form of $2\left(x+4\right)$is $\mathbf{2}\mathit{x}\mathbf{+}\mathbf{8}$.

Step-by-step solution

Step 1. Use the distributive property.

The distributive law of multiplication over addition or subtraction states that, $a\left(b\pm c\right)=ab\pm ac$.

So, the values of $a,b,\mathrm{and}c$should be as follows:

$\begin{array}{l}a=2\\ b=x\\ c=4\end{array}$

Step 2. Rewrite the expression.

Use the distributive property to expand the expression further as shown below:

$2\left(x+4\right)\text{=}\left(\text{2}\right)\text{x+}\left(\text{2}\right)4$

Step 3. Evaluate the expression.

To simplify further, multiply the numbers and solve further as shown below:

$\begin{array}{l}2\left(\mathrm{x}+4\right)\mathrm{=}\left(\mathrm{2}\right)\mathrm{x}+\left(\mathrm{2}\right)4\left[\mathrm{Multiply}\right]\\ =2\mathrm{x}+8\end{array}$