Question

Evaluate the following expression and name the property used in each step:

$\left(8-2^3\right)+21$

Short answer

The value of the expression is:$\left(8-2^3\right)+21=21$

Step-by-step solution

Step 1. Given information.

The given expression is:

$\left(8-2^3\right)+21$

Step 2. Write the concept.

The substitution property for multiplication, addition and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a÷b=c\\ a\pm b=c\end{array}$

The property of additive inverse is:

$a+\left(-a\right)=0$

And use the formula such that $a^3=a\times a\times a$.

Step 3. Evaluate the expression.

The expression can be written as in below:

$$\begin{gathered} \left(8-2^3\right)+21=\left(8-8\right)+21 \\ \begin{array}{c}=\left(8+\left(-8\right)\right)+21\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Additive\hspace{0.17em}\hspace{0.17em}Inverse}\right]\end{array} \\ =0+21\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right] \\ =21 \end{gathered}$$