Let's evaluate the expression step by step and identify Bassima's error. The original mathematical expression is:
[tex]\[ 2(12 - 14)^2 - (-5) + 12 \][/tex]
We'll go through this step by step:
1. Evaluate inside the parentheses first:
[tex]\[ 12 - 14 = -2 \][/tex]
2. Square the result inside the parentheses:
[tex]\[ (-2)^2 = 4 \][/tex]
3. Multiply by 2:
[tex]\[ 2 \times 4 = 8 \][/tex]
4. Negate the -5:
[tex]\[ -(-5) = 5 \][/tex]
5. Add the results together:
[tex]\[ 8 + 5 + 12 = 25 \][/tex]
Thus, the correct evaluation of the expression is:
[tex]\[ 2(12 - 14)^2 - (-5) + 12 = 25 \][/tex]
Now let's review Bassima's steps:
1. Bassima's first step:
[tex]\[ 2(12 - 14)^2 - (-5) + 12 \][/tex]
[tex]\[ 2(-2)^2 - (-5) + 12 \][/tex]
2. Bassima's second step:
[tex]\[ 2(-4) - (-5) + 12 \][/tex]
This step is where Bassima made an error. The correct value of [tex]\((-2)^2\)[/tex] is 4, not -4. Bassima evaluated [tex]\((-2)^2\)[/tex] as -4.
3. Bassima's third step:
[tex]\[ 2(-4) - (-5) + 12 \][/tex]
[tex]\[ -8 + 5 + 12 \][/tex]
4. Bassima's final step:
[tex]\[ -8 + 5 + 12 = 9 \][/tex]
Bassima's error occurred when she incorrectly evaluated [tex]\((-2)^2\)[/tex] as -4 instead of 4.
Bassima's error was:
[tex]\[ \text{Bassima evaluated } (-2)^2 \text{ as } -4 . \][/tex]
This is the correct identification of her mistake.
