Simplify `(81x^(2)-49 y^(2))/(9x + 7y)`
A. `9x+7y`
B. `9x- 7y`
C. 9x
D. 7y

Options

A. C
B. A
C. B
D. D

Answer

To simplify the expression \((81x^2 - 49y^2)/(9x + 7y)\), we can follow these steps:

### Step 1: Recognize the difference of squares
The expression in the numerator, \(81x^2 - 49y^2\), is a difference of squares. We can use the formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
where \(a = 9x\) and \(b = 7y\).

### Step 2: Apply the difference of squares formula
Using the formula, we can rewrite the numerator:
\[ 81x^2 - 49y^2 = (9x)^2 - (7y)^2 = (9x - 7y)(9x + 7y) \]

### Step 3: Substitute back into the expression
Now we substitute this back into our original expression:
\[ \frac{(9x - 7y)(9x + 7y)}{9x + 7y} \]

### Step 4: Cancel the common terms
We can cancel \(9x + 7y\) from the numerator and the denominator:
\[ 9x - 7y \]

### Step 5: Final result
Thus, the simplified form of the expression is:
\[ 9x - 7y \]

### Conclusion
The correct answer is option B: \(9x - 7y\).

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