To determine which of the given expressions is equivalent to [tex]\(9^2 + 4^2\)[/tex], let's evaluate each of them step-by-step.
First, let's calculate [tex]\(9^2 + 4^2\)[/tex]:
[tex]\[
9^2 = 81 \quad \text{and} \quad 4^2 = 16
\][/tex]
[tex]\[
9^2 + 4^2 = 81 + 16 = 97
\][/tex]
Now, we need to evaluate each of the given expressions to see which one matches 97.
1. [tex]\((9 \times 9) + (4 \times 4)\)[/tex]:
[tex]\[
9 \times 9 = 81 \quad \text{and} \quad 4 \times 4 = 16
\][/tex]
[tex]\[
(9 \times 9) + (4 \times 4) = 81 + 16 = 97
\][/tex]
2. [tex]\((9 + 9) + (4 + 4)\)[/tex]:
[tex]\[
9 + 9 = 18 \quad \text{and} \quad 4 + 4 = 8
\][/tex]
[tex]\[
(9 + 9) + (4 + 4) = 18 + 8 = 26
\][/tex]
3. [tex]\((9 + 4)^2\)[/tex]:
[tex]\[
9 + 4 = 13
\][/tex]
[tex]\[
(9 + 4)^2 = 13^2 = 169
\][/tex]
4. [tex]\((9 \times 4)^2\)[/tex]:
[tex]\[
9 \times 4 = 36
\][/tex]
[tex]\[
(9 \times 4)^2 = 36^2 = 1296
\][/tex]
Comparing all these results with [tex]\(97\)[/tex], we see that the expression [tex]\((9 \times 9) + (4 \times 4)\)[/tex] is equivalent to [tex]\(9^2 + 4^2\)[/tex].
Thus, the correct choice is:
[tex]\((9 \times 9) + (4 \times 4)\)[/tex].
