2 min read Jun 17, 2024

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.