To evaluate the expression [tex]\( 5x - (x+3)^2 \)[/tex] for [tex]\( x = 2 \)[/tex], let's go through the steps carefully and identify where Amir made a mistake and what the correct calculation should be.
### Amir's Calculation:
[tex]\[
\begin{aligned}
5(2) - (2 + 3)^2 & = 10 + (-5)^2 \\
& = 10 + 25 \\
& = 35
\end{aligned}
\][/tex]
### Correct Calculation:
1. Substitute [tex]\( x = 2 \)[/tex] into the expression:
[tex]\[
5x - (x + 3)^2 \implies 5(2) - (2 + 3)^2
\][/tex]
2. Calculate the first part, [tex]\( 5x \)[/tex]:
[tex]\[
5(2) = 10
\][/tex]
3. Calculate the second part, [tex]\((x + 3)^2\)[/tex]:
[tex]\[
(2 + 3)^2 = 5^2 = 25
\][/tex]
4. Combine the results from the two parts:
[tex]\[
10 - 25
\][/tex]
5. Perform the final subtraction:
[tex]\[
10 - 25 = -15
\][/tex]
### Conclusion:
The mistake Amir made was in the sign and interpretation of the square. Specifically, he incorrectly added [tex]\((-5)^2\)[/tex] instead of correctly calculating [tex]\((2 + 3)^2\)[/tex] and then subtracting the result. The correct calculation shows that:
[tex]\[
5(2) - (2 + 3)^2 = 10 - 25 = -15
\][/tex]
Thus, the correct answer is [tex]\(-15\)[/tex].
