Q4. - Algebra 2

Question

4. Evaluate $a^3+b\left(9-c\right)$ if  $a=-2,b=\frac{1}{3},$ and $c=-12$

Step-by-Step Solution

Answer

Expression $a^3+b\left(9-c\right)$ results into $-1$

Step 1 - Order for simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 2 - Substitution

Substitute $-2$ for a, $\frac{1}{3}$ for b, and $-12$ for c in given expression.

 $a^3+b\left(9-c\right)={\left(-2\right)}^3+\frac{1}{3}\left(9-\left(-12\right)\right)$

Step 3 - Simplify expression inside grouping symbol

To evaluate the value of the given expression, first simplify parentheses as shown below

$\begin{array}{c}{\left(-2\right)}^3+\frac{1}{3}\left(9-\left(-12\right)\right)=-8+\frac{1}{3}\left(9+12\right)\\ =-8+\frac{1}{3}\left(21\right)\\ =-8+7\end{array}$

Step 4 - Add - 8 with 7

Now, to simplify further add the numbers to get, 

$-8+7=-1$