Chapter 12, Problem 18CLR

To determine

To Evaluate: The simplified value of the expression $a-2\left(3a-2\right)$ .

Answer to Problem 18CLR

The value of the expression $a-2\left(3a-2\right)$ is $-5a+4$ .

Explanation of Solution

Given information:

The expression is $a-2\left(3a-2\right)$ .

Formula used:

When an algebraic expression multiply by group of algebraic terms connected with addition or subtraction is equal to multiplication of expression with the terms separately. That is $a\left(b\pm c\right)=\left(a\times b\right)\pm \left(a\times c\right)$

If two terms have the same sign, their product is positive.

If two terms have the opposite sign, their product is negative.

Calculation:

Consider the expression is $a-2\left(3a-2\right)$ .

Recall that when an algebraic expression multiply by group of algebraic terms connected with addition or subtraction is equal to multiplication of expression with the terms separately. That is $a\left(b\pm c\right)=\left(a\times b\right)\pm \left(a\times c\right)$

Use it,

  $a-2\left(3a-2\right)=a+\left(\left(-2\times 3a\right)+\left(-2\times \left(-2\right)\right)\right)$

Again recall that If two terms have the same sign, their product is positive and

if two terms have the opposite sign, their product is negative.

Apply it,

  $\begin{array}{c}a+\left(\left(-2\times 3a\right)+\left(-2\times \left(-2\right)\right)\right)=a-6a+4\\ =-5a+4\end{array}$

Thus, the value of the expression $a-2\left(3a-2\right)$ is $-5a+4$ .