Q42. - Algebra 1

Question

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

$\left(8-3\right)4$

Step-by-Step Solution

Answer

The value of given expression is $20$.

Step 1. Distributive property.

If $a,b$ and $c$ are three real numbers then $a·\left(b+c\right)=a·b+a·c$ and $\left(b+c\right)·a=b·a+c·a$

Step 2. Application of distribution property.

$$\begin{gathered} \left(8-3\right)4=\left(8+\left(-3\right)\right)4 \\ =8·4+\left(-3\right)·4 \left[\mathrm{By} \mathrm{Distribution} \mathrm{property}\right] \end{gathered}$$

Step 3. Simplifying the expression.

$$\begin{gathered} 8·4+\left(-3\right)·4=32-12 \left[\mathrm{Performing} \mathrm{multiplication}\right] \\ =20 \left[\mathrm{Performing} \mathrm{subtraction}\right] \end{gathered}$$