Chapter R.18, Problem 1DE

Find an equivalent expression without parentheses.

$-\left(-2c\right)$

To determine

To calculate: The equivalent expression of the expression $-\left(-2c\right)$ without parenthesis.

Answer to Problem 1DE

Solution:

The equivalent expression of the expression $-\left(-2c\right)$ is $\underset{\_}{2c}$.

Explanation of Solution

Given information:

The provided expression is $-\left(-2c\right)$.

Formula used:

By the property of $-1$, for any number a,

$-1\cdot a=-a$

The associative law of multiplication states that, for any numbers $a,b$ and $c$ the grouping in any order of multiplication does not affect the answer, that is:

$\left(ab\right)c=a\left(bc\right)$

Calculation:

Consider the expression,

$-\left(-2c\right)$

The negative sign outside the brackets refers to the opposite of it.

Multiply the whole expression inside by $-1$, by the use of property of $-1$ to find the opposite as below:

$-\left(-2c\right)=-1\cdot \left(-2c\right)$

Use the associative law, to simplify as below:

$\begin{array}{c}-\left(-2c\right)=-1\cdot \left(-2c\right)\\ =\left(-1\cdot -2\right)c\\ =2c\end{array}$

Hence, the expression equivalent of the expression $-\left(-2c\right)$ is $2c$.