Chapter 6, Problem 9QC

To determine

To Rewrite: The polynomial expression $-\frac{3}{4}\left(3z+5\right)$ without parentheses.

Answer to Problem 9QC

The new expression is $-\frac{9}{4}z-\frac{15}{4}$ .

Explanation of Solution

Given information:

The expression is $-\frac{3}{4}\left(3z+5\right)$ .

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 .

Calculation:

Consider the expression $-\frac{3}{4}\left(3z+5\right)$ .

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,

  $-\frac{3}{4}\left(3z+5\right)=-\frac{3}{4}\times 3z+\left(-\frac{3}{4}\right)\times 5$

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

Further simplify,

  $-\frac{3}{4}\times 3z+\left(-\frac{3}{4}\right)\times 5=-\frac{9}{4}z-\frac{15}{4}$

Thus, the expression can be rewrite as $-\frac{9}{4}z-\frac{15}{4}$ .