To determine Sandy's error, let's evaluate the expression [tex]\( (-2)^3(6-3) - 5(2+3) \)[/tex] step-by-step and compare it with Sandy's calculations.
1. Evaluate inside the parentheses:
- For [tex]\( (6-3) \)[/tex]:
[tex]\[
6 - 3 = 3
\][/tex]
- For [tex]\( (2+3) \)[/tex]:
[tex]\[
2 + 3 = 5
\][/tex]
The expression now becomes:
[tex]\[
(-2)^3 \times 3 - 5 \times 5
\][/tex]
2. Evaluate the exponentiation:
- For [tex]\( (-2)^3 \)[/tex]:
[tex]\[
(-2)^3 = -8
\][/tex]
The expression now becomes:
[tex]\[
-8 \times 3 - 5 \times 5
\][/tex]
3. Perform the multiplication:
- For [tex]\( -8 \times 3 \)[/tex]:
[tex]\[
-8 \times 3 = -24
\][/tex]
- For [tex]\( 5 \times 5 \)[/tex]:
[tex]\[
5 \times 5 = 25
\][/tex]
The expression now becomes:
[tex]\[
-24 - 25
\][/tex]
4. Perform the subtraction:
[tex]\[
-24 - 25 = -49
\][/tex]
Sandy's steps were:
[tex]\[
(-2)^3(3) - 5(5)
\][/tex]
[tex]\[
8(3) - 25
\][/tex]
[tex]\[
24 - 25
\][/tex]
[tex]\[
-1
\][/tex]
Comparing this to our step-by-step evaluation, we see that Sandy made an error in evaluating [tex]\( (-2)^3 \)[/tex] as [tex]\( 8 \)[/tex] instead of [tex]\( -8 \)[/tex]. This incorrect calculation led to Sandy getting the wrong final answer.
Thus, the correct answer is:
Sandy should have evaluated [tex]\((-2)^3\)[/tex] as -8.
