Q41. - Algebra 1

Question

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

$-2\left(5-3\right)$

Step-by-Step Solution

Answer

The value of given expression is $-4$.

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.

$$\begin{gathered} -2\left(5-3\right)=\left(-2\right)\left(5+\left(-3\right)\right) \\ =\left(-2\right)·5+\left(-2\right)·\left(-3\right) \left[\mathrm{By} \mathrm{Distribution} \mathrm{property}\right] \end{gathered}$$

Step 3. Simplifying the expression.

$$\begin{gathered} \left(-2\right)·5+\left(-2\right)·\left(-3\right)=-10+6 \left[\mathrm{Performing} \mathrm{multiplication}\right] \\ =-4 \left[\mathrm{Performing} \mathrm{addition}\right] \end{gathered}$$