`9a^(4)+12a^(2)b^(2)+4b^(4)`
Which of the following is equivalent to the expression shown above?

Options

A. `(3a^(2)+2b^(2))^(2)`
B. `(3a+2b)^(4)`
C. `(9a^(2)+4b^(2))^(2)`
D. `(9a+4b)^(4)`

Explanation

To solve the expression \( 9a^{4} + 12a^{2}b^{2} + 4b^{4} \) and find its equivalent form, we can follow these steps:

### Step 1: Rewrite the terms
We can rewrite the first term \( 9a^{4} \) as \( (3a^{2})^{2} \).

### Step 2: Rewrite the middle term
The middle term \( 12a^{2}b^{2} \) can be expressed as \( 2 \cdot 3a^{2} \cdot 2b^{2} \).

...