Q33. - Algebra 1

Question

Simplify each expression. If not possible, write simplified.

$\mathbf{(}\mathbf{2}\mathbf{ }\mathbf{–}\mathbf{ }\mathbf{4}\mathit{n}\mathbf{)}\mathbf{17}$

Step-by-Step Solution

Answer

The simplified form of $(2-4n)17$ is $\mathbf{34}\mathbf{-}\mathbf{68}\mathit{n}$.

Step 1. Use the distributive property.

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

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

$\begin{array}{l}a=2\\ b=4n\\ c=17\end{array}$

Step 2. Rewrite the expression.

$(2-4n)17=\left(2\right)17-\left(4n\right)17$

Step 3. Simplify the expression.

A simplified expression does not contain any like terms or parentheses.

$\begin{array}{l}(2-4n)17=\left(2\right)17-\left(4n\right)17 \left[Multiply\right]\\ \text{=34-68n}\\ \text{=95}\end{array}$