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

Options

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

Answer

To solve the expression `(9x^2 + 8xy - 4) - (7x^2 - 2xy + 2)`, we will simplify it step by step.

### 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
Now we will combine the like terms. We will group the \(x^2\) terms, the \(xy\) terms, and the constant terms separately:
- For \(x^2\) terms: \(9x^2 - 7x^2\)
- For \(xy\) terms: \(8xy + 2xy\)
- For constant terms: \(-4 - 2\)

Calculating each group:
- \(9x^2 - 7x^2 = 2x^2\)
- \(8xy + 2xy = 10xy\)
- \(-4 - 2 = -6\)

### Step 3: Write the final expression
Putting it all together, we have:
\[ 2x^2 + 10xy - 6 \]

Thus, the simplified expression is:
\[ \boxed{2x^2 + 10xy - 6} \]

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