Let's examine each of the given options to determine which is equivalent to [tex]\(9^2 + 4^2\)[/tex]:
1. Calculate the original expression [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]
So, the value of the original expression is 97.
2. Evaluate each of the given options:
- Option 1: [tex]\((9 \times 4)^2\)[/tex]
[tex]\[
9 \times 4 = 36
\][/tex]
[tex]\[
36^2 = 1296
\][/tex]
So, the value of this option is 1296.
- Option 2: [tex]\((9 + 4)^2\)[/tex]
[tex]\[
9 + 4 = 13
\][/tex]
[tex]\[
13^2 = 169
\][/tex]
So, the value of this option is 169.
- Option 3: [tex]\((9 + 9) + (4 + 4)\)[/tex]
[tex]\[
9 + 9 = 18 \quad \text{and} \quad 4 + 4 = 8
\][/tex]
[tex]\[
18 + 8 = 26
\][/tex]
So, the value of this option is 26.
- Option 4: [tex]\((9 \times 9) + (4 \times 4)\)[/tex]
[tex]\[
9 \times 9 = 81 \quad \text{and} \quad 4 \times 4 = 16
\][/tex]
[tex]\[
81 + 16 = 97
\][/tex]
So, the value of this option is 97.
3. Compare the calculated values:
- [tex]\(1296\)[/tex] (option 1)
- [tex]\(169\)[/tex] (option 2)
- [tex]\(26\)[/tex] (option 3)
- [tex]\(97\)[/tex] (option 4)
Out of these, the only value that matches the original expression [tex]\(97\)[/tex] is from option 4.
Therefore, the correct answer is:
[tex]\((9 \times 9) + (4 \times 4)\)[/tex]
