(xy%2B1)(x%2B3).jpeg "(xy-1)(xy+1)(x+3)")
Factoring and Simplifying: (xy-1)(xy+1)(x+3)
This expression involves three factors: (xy-1), (xy+1), and (x+3). To simplify this, we can use the following:
Recognizing the Difference of Squares
The first two factors, (xy-1) and (xy+1), are in the form of a difference of squares. Recall that:
a² - b² = (a + b)(a - b)
Applying this to our factors:
- (xy-1) = (xy)² - 1²
- (xy+1) = (xy)² + 1²
Therefore, we can rewrite the entire expression as:
(xy)² - 1²)(xy)² + 1²)(x+3)
Expanding and Simplifying
Now, we can expand the first two factors using the difference of squares pattern:
- [(xy)² - 1²][(xy)² + 1²] = (xy)⁴ - 1⁴
This simplifies to:
(x⁴y⁴ - 1)(x+3)
Final Result
The fully factored and simplified form of the expression (xy-1)(xy+1)(x+3) is (x⁴y⁴ - 1)(x+3).
This can be further expanded if desired, but it is generally considered simplified in its current form.