Solve `(9x+7xy +9x^(2)) + (8+x^(2) -xy -y^(2)+1)`.

Options

A. `16xy + 8x^(2) + xy + y^(2) +9`
B. `16xy + 10x^(2) + xy + y^(2) +9`
C. `16xy + 10x^(2) -xy -y^(2) -9`
D. `16xy + 10x^(2) -xy -y^(2) +9`

Answer

To solve the expression `(9x + 7xy + 9x^2) + (8 + x^2 - xy - y^2 + 1)`, we will follow these steps:

### Step 1: Remove the parentheses
We start by rewriting the expression without the parentheses. Since we are adding, we can simply write:

\[ 9x + 7xy + 9x^2 + 8 + x^2 - xy - y^2 + 1 \]

### Step 2: Combine like terms
Next, we will group the like terms together. The like terms are those that have the same variables raised to the same powers.

1. **Terms with \(x^2\)**:
- \(9x^2 + x^2 = 10x^2\)

2. **Terms with \(xy\)**:
- \(7xy - xy = 6xy\)

3. **Terms with \(x\)**:
- \(9x\) (there are no other \(x\) terms)

4. **Constant terms**:
- \(8 + 1 = 9\)

5. **Terms with \(y^2\)**:
- \(-y^2\) (there are no other \(y^2\) terms)

### Step 3: Write the final expression
Now we can combine all the results from the previous step:

\[ 10x^2 + 6xy + 9x - y^2 + 9 \]

### Final Answer:
Thus, the simplified expression is:

\[ 10x^2 + 6xy + 9x - y^2 + 9 \]

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