Which of these is equivalent to [tex]$9^2 + 4^2?$[/tex]

A. [tex]$(9 + 4)^2$[/tex]

B. [tex][tex]$(9 \times 4)^2$[/tex][/tex]

C. [tex]$(9 \times 9) + (4 \times 4)$[/tex]

D. [tex]$(9 + 9) + (4 + 4)$[/tex]



Answer :

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]