Let's walk through the correct steps to evaluate the expression [tex]\(2(12-14)^2-(-5)+12\)[/tex] and identify where Bassima made a mistake.
1. Evaluate inside the parentheses:
[tex]\[
12 - 14 = -2
\][/tex]
2. Square the result:
[tex]\[
(-2)^2 = 4
\][/tex]
3. Multiply by 2:
[tex]\[
2 \times 4 = 8
\][/tex]
4. Evaluate [tex]\(-(-5)\)[/tex]:
[tex]\[
-(-5) = 5
\][/tex]
5. Add the results and 12:
[tex]\[
8 + 5 + 12 = 25
\][/tex]
So, the correct final result is [tex]\(25\)[/tex].
Bassima’s steps were:
- [tex]\( 2(12-14)^2-(-5)+12 \)[/tex]
- [tex]\( 2(-2)^2-(-5)+12 \)[/tex]
- [tex]\( 2(-4)-(-5)+12 \)[/tex]
- [tex]\( -8+5+12 \)[/tex]
- [tex]\( 9 \)[/tex]
The error occurred when Bassima evaluated [tex]\((-2)^2\)[/tex]. Instead of correctly evaluating [tex]\((-2)^2\)[/tex] as [tex]\(4\)[/tex], Bassima evaluated it incorrectly as [tex]\(-4\)[/tex].
Therefore, Bassima's error was:
Bassima evaluated [tex]\((-2)^2\)[/tex] as -4.
