Chapter 6, Problem 7QC

To determine

To Rewrite: The polynomial expression $-1\left(13b^2+2b-1\right)$ without parentheses.

Answer to Problem 7QC

The new expression is $-13b^2-2b+1$ .

Explanation of Solution

Given information:

The expression is $-1\left(13b^2+2b-1\right)$ .

Formula used:

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

  $a\left(b\pm c\pm d\right)=ab\pm ac\pm ad$

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 $-1\left(13b^2+2b-1\right)$ .

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

  $a\left(b\pm c\pm d\right)=ab\pm ac\pm ad$

Use it,

  $-1\left(13b^2+2b-1\right)=-1\times 13b^2+\left(-1\right)\times 2b+\left(-1\right)\times \left(-1\right)$

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,

  $-1\times 13b^2+\left(-1\right)\times 2b+\left(-1\right)\times \left(-1\right)=-13b^2-2b+1$

Thus, the expression can be rewrite as $-13b^2-2b+1$ .