(5x-3)-(2x-5)%5E2.jpeg "(5x+3)(5x-3)-(2x-5)^2")
Expanding and Simplifying the Expression (5x+3)(5x-3)-(2x-5)^2
This article will guide you through the process of expanding and simplifying the algebraic expression: (5x+3)(5x-3)-(2x-5)^2.
Expanding the Expressions
Let's break down the expression into its components:
-
(5x+3)(5x-3): This is a product of two binomials in the form (a+b)(a-b). We can use the difference of squares pattern to expand it:
- (a+b)(a-b) = a^2 - b^2
- Therefore, (5x+3)(5x-3) = (5x)^2 - (3)^2 = 25x^2 - 9
-
(2x-5)^2: This is a square of a binomial. We can use the square of a binomial pattern to expand it:
- (a-b)^2 = a^2 - 2ab + b^2
- Therefore, (2x-5)^2 = (2x)^2 - 2(2x)(5) + (5)^2 = 4x^2 - 20x + 25
Combining the Expanded Terms
Now, we can substitute the expanded forms back into the original expression:
(5x+3)(5x-3)-(2x-5)^2 = (25x^2 - 9) - (4x^2 - 20x + 25)
Finally, we can simplify the expression by combining like terms:
25x^2 - 9 - 4x^2 + 20x - 25 = 21x^2 + 20x - 34
Conclusion
Therefore, the simplified form of the expression (5x+3)(5x-3)-(2x-5)^2 is 21x^2 + 20x - 34.