Question

In Exercises 23-28, use properties of real numbers to write the expression without parentheses.

$-\frac{5}{2}\left(2x-4y\right)$

Short answer

The expression can be rewritten as $-5x+10y$.

Step-by-step solution

Step 1. Definition of the distributive property.

The distributive property is the property in which when a number is multiplied by the difference of two number gives the same result as if the number is multiplied by each of the terms and then subtract the result.

Step 2. Concept of the property used.

The expression can also be written as the difference of the result obtained by the product of $-5/2$and $2x,-5/2$and $-4y$.

Step 3. using the property.

Multiply$-5/2$ with the terms written in the bracket.

$\begin{array}{l}=-\frac{5}{2}\left(2x-4y\right)\\ =\frac{-5}{2}\left(2x\right)+\frac{5}{2}\left(4y\right)\\ =-5x+10y\end{array}$