Evaluate :
`3x^(2) + 5xy - 4y^(2) + x^(2) - 8xy - 5y^(2)`

Options

A. `4x^(2) + 3xy - 9y^(2)`
B. `4x^(2) - 3xy - 9y^(2)`
C. `4x^(2) - 3xy + 9y^(2)`
D. `4x^(2) + 3xy + 9y^(2)`

Answer

To evaluate the expression \(3x^{2} + 5xy - 4y^{2} + x^{2} - 8xy - 5y^{2}\), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ 3x^{2} + 5xy - 4y^{2} + x^{2} - 8xy - 5y^{2} \]

### Step 2: Group the like terms
Next, we identify and group the like terms in the expression. The like terms are:
- \(x^{2}\) terms: \(3x^{2}\) and \(x^{2}\)
- \(xy\) terms: \(5xy\) and \(-8xy\)
- \(y^{2}\) terms: \(-4y^{2}\) and \(-5y^{2}\)

So we can rewrite the expression as:
\[ (3x^{2} + x^{2}) + (5xy - 8xy) + (-4y^{2} - 5y^{2}) \]

### Step 3: Combine the like terms
Now we will combine the like terms:
1. For \(x^{2}\) terms:
\[ 3x^{2} + x^{2} = 4x^{2} \]

2. For \(xy\) terms:
\[ 5xy - 8xy = -3xy \]

3. For \(y^{2}\) terms:
\[ -4y^{2} - 5y^{2} = -9y^{2} \]

### Step 4: Write the final expression
Now we can write the final simplified expression by combining all the results:
\[ 4x^{2} - 3xy - 9y^{2} \]

### Final Answer:
The evaluated expression is:
\[ 4x^{2} - 3xy - 9y^{2} \]

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