Chapter 6, Problem 8QC

To determine

To Rewrite: The polynomial expression $-\frac{1}{2}\left(2m-5\right)$ without parentheses.

Answer to Problem 8QC

The new expression is $-m+\frac{5}{2}$ .

Explanation of Solution

Given information:

The expression is $-\frac{1}{2}\left(2m-5\right)$ .

Formula used:

Distribution property states that multiplication of a term with sum or difference of two other terms same as add or subtract them separately after multiplication. That is

  $a\left(b\pm c\right)=ab\pm ac$

Multiplication of a negative and a positive term is always negative one and a negative and a negative term is always positive one.

Calculation:

Consider the expression $-\frac{1}{2}\left(2m-5\right)$ .

Recall that distribution property states that multiplication of a term with sum or difference of two other terms same as add or subtract them separately after multiplication. That is

  $a\left(b\pm c\right)=ab\pm ac$

Use it,

  $-\frac{1}{2}\left(2m-5\right)=-\frac{1}{2}\times 2m+\left(-\frac{1}{2}\right)\times \left(-5\right)$

Again recall that multiplication of a negative and a positive term is always negative one and a negative and a negative term is always positive one.

Further simplify,

  $-\frac{1}{2}\times 2m+\left(-\frac{1}{2}\right)\times \left(-5\right)=-m+\frac{5}{2}$

Thus, the expression can be rewrite as $-m+\frac{5}{2}$ .