Q46. - Algebra 1

Question

Rewrite each expression using the distributive property. Then simplify.

$-4\left(5-2t\right)$

Step-by-Step Solution

Answer

The simplified expression is $8t-20$.

Step 1. Distributive property.

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

Step 2. Application of distribution property.

Apply the distributive property to get

$$\begin{gathered} -4\left(5-2t\right)=\left(-4\right)\left(5+\left(-2t\right)\right) \\ =\left(-4\right)·5+\left(-4\right)·\left(-2t\right) \left[\mathrm{By} \mathrm{Distribution} \mathrm{property}\right] \end{gathered}$$

Step 3. Simplifying the expression.

Simplify further by multiplying the numbers to get

$$\begin{gathered} \left(-4\right)·5+\left(-4\right)·\left(-2t\right)=-20+8t \\ =8t-20 \end{gathered}$$