(2x%2B3y-4).jpeg "(2x+3y+4)(2x+3y-4)")
Factoring the Expression (2x + 3y + 4)(2x + 3y - 4)
This expression represents the product of two binomials that are very similar, differing only in the sign of the last term. This pattern is a classic example of the difference of squares factorization.
Understanding the Difference of Squares
The difference of squares factorization states that: (a + b)(a - b) = a² - b²
In our expression, we can see that:
- a = 2x + 3y
- b = 4
Applying the Formula
Let's substitute these values into the difference of squares formula:
(2x + 3y + 4)(2x + 3y - 4) = (2x + 3y)² - 4²
Now, we need to expand the square:
(2x + 3y)² - 4² = (2x + 3y)(2x + 3y) - 16
Finally, we expand the remaining product:
(2x + 3y)(2x + 3y) - 16 = 4x² + 12xy + 9y² - 16
Result
Therefore, the factored form of (2x + 3y + 4)(2x + 3y - 4) is 4x² + 12xy + 9y² - 16.
Key Takeaways
- Recognizing the difference of squares pattern simplifies factoring.
- The pattern applies when two binomials differ only in the sign of the last term.
- Factoring allows us to rewrite expressions in a more compact and often more useful form.