Solve `(9x^(2) + 8xy-4)-(7x^(2) -2xy +2)`.

Options

A. `2x^(2)+ 10xy-6`
B. `2x^(2) -10xy -8`
C. `2x^(2) + 10xy - 8`
D. `2x^(2) -10xy + 6`

Answer

To solve the expression \( (9x^{2} + 8xy - 4) - (7x^{2} - 2xy + 2) \), we will follow these steps:

### Step 1: Distribute the negative sign
We start by distributing the negative sign across the second set of parentheses:
\[ (9x^{2} + 8xy - 4) - (7x^{2} - 2xy + 2) = 9x^{2} + 8xy - 4 - 7x^{2} + 2xy - 2 \]

### Step 2: Combine like terms
Next, we will combine the like terms:
- For \(x^{2}\) terms: \(9x^{2} - 7x^{2}\)
- For \(xy\) terms: \(8xy + 2xy\)
- For constant terms: \(-4 - 2\)

Calculating each:
\[ 9x^{2} - 7x^{2} = 2x^{2} \]
\[ 8xy + 2xy = 10xy \]
\[ -4 - 2 = -6 \]

### Step 3: Write the final expression
Now, we can write the final simplified expression:
\[ 2x^{2} + 10xy - 6 \]

### Final Answer
Thus, the solution to the expression is:
\[ 2x^{2} + 10xy - 6 \]

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