Simplify: `(3y)^(2)+x^(2)-(2y)^(2)`

Options

A. `x^(2)-5y^(2)`
B. `x^(2)+y^(2)`
C. `x^(2)-y^(2)`
D. `x^(2)+5y^(2)`

Answer

To simplify the expression \( (3y)^{2} + x^{2} - (2y)^{2} \), we can follow these steps:

### Step 1: Expand the squared terms
First, we will expand the squared terms in the expression.

\[ (3y)^{2} = 9y^{2} \]
\[ (2y)^{2} = 4y^{2} \]

So, the expression becomes:
\[ 9y^{2} + x^{2} - 4y^{2} \]

### Step 2: Combine like terms
Next, we will combine the like terms. We have \( 9y^{2} \) and \( -4y^{2} \).

\[ 9y^{2} - 4y^{2} = 5y^{2} \]

Now, substitute this back into the expression:
\[ 5y^{2} + x^{2} \]

### Final Result
Thus, the simplified expression is:
\[ 5y^{2} + x^{2} \]

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