To solve the problem, we need to find which expression is equivalent to [tex]\(9^2 + 4^2\)[/tex].
Let's start by evaluating [tex]\(9^2 + 4^2\)[/tex].
[tex]\[ 9^2 \][/tex] means 9 multiplied by itself, which is:
[tex]\[ 9 \times 9 = 81 \][/tex]
[tex]\[ 4^2 \][/tex] means 4 multiplied by itself, which is:
[tex]\[ 4 \times 4 = 16 \][/tex]
Adding them together:
[tex]\[ 81 + 16 = 97 \][/tex]
Now we will check each provided option to find which one equals 97.
1. [tex]\((9 + 4)^2\)[/tex]
[tex]\[ 9 + 4 = 13 \][/tex]
[tex]\[ 13^2 = 13 \times 13 = 169 \][/tex]
This is not equivalent to 97.
2. [tex]\((9 \times 4)^2\)[/tex]
[tex]\[ 9 \times 4 = 36 \][/tex]
[tex]\[ 36^2 = 36 \times 36 = 1296 \][/tex]
This is not equivalent to 97.
3. [tex]\((9 \times 9) + (4 \times 4)\)[/tex]
[tex]\[ 9 \times 9 = 81 \][/tex]
[tex]\[ 4 \times 4 = 16 \][/tex]
Adding them together:
[tex]\[ 81 + 16 = 97 \][/tex]
This is equivalent to 97.
4. [tex]\((9 + 9) + (4 + 4)\)[/tex]
[tex]\[ 9 + 9 = 18 \][/tex]
[tex]\[ 4 + 4 = 8 \][/tex]
Adding them together:
[tex]\[ 18 + 8 = 26 \][/tex]
This is not equivalent to 97.
After careful evaluation, the expression that is equivalent to [tex]\(9^2 + 4^2\)[/tex] is [tex]\((9 \times 9) + (4 \times 4)\)[/tex].
Thus, the correct answer is:
[tex]\[
(9 \times 9) + (4 \times 4)
\][/tex]
