(2x%2B5)-(2x-5)2.jpeg "(2x-5)(2x+5)-(2x-5)2")
Simplifying the Expression: (2x - 5)(2x + 5) - (2x - 5)^2
This article will guide you through the steps of simplifying the algebraic expression: (2x - 5)(2x + 5) - (2x - 5)^2. We will use the following key algebraic concepts:
- Difference of Squares: (a + b)(a - b) = a² - b²
- Squaring a Binomial: (a - b)² = a² - 2ab + b²
Step 1: Apply the Difference of Squares Formula
The first part of the expression, (2x - 5)(2x + 5), is in the form of (a - b)(a + b). Applying the difference of squares formula, we get:
(2x - 5)(2x + 5) = (2x)² - (5)² = 4x² - 25
Step 2: Expand the Squared Term
The second part of the expression, (2x - 5)², is in the form of (a - b)². Applying the squaring a binomial formula, we get:
(2x - 5)² = (2x)² - 2(2x)(5) + (5)² = 4x² - 20x + 25
Step 3: Combine the Results
Now, we can substitute the simplified expressions back into the original expression:
(2x - 5)(2x + 5) - (2x - 5)² = (4x² - 25) - (4x² - 20x + 25)
Step 4: Simplify the Expression
Finally, we simplify the expression by distributing the negative sign and combining like terms:
4x² - 25 - 4x² + 20x - 25 = 20x - 50
Conclusion
Therefore, the simplified form of the expression (2x - 5)(2x + 5) - (2x - 5)² is 20x - 50.