(5x-2)-2(5x-3)(x%2B1).jpeg "(2x+3)(5x-2)-2(5x-3)(x+1)")
Simplifying the Expression (2x+3)(5x-2)-2(5x-3)(x+1)
This article will guide you through the process of simplifying the algebraic expression: (2x+3)(5x-2)-2(5x-3)(x+1).
Step 1: Expand the Products
We begin by expanding the products using the distributive property (or FOIL method).
- (2x+3)(5x-2) = (2x * 5x) + (2x * -2) + (3 * 5x) + (3 * -2) = 10x² - 4x + 15x - 6
- (5x-3)(x+1) = (5x * x) + (5x * 1) + (-3 * x) + (-3 * 1) = 5x² + 5x - 3x - 3
Now our expression becomes: 10x² - 4x + 15x - 6 - 2(5x² + 5x - 3x - 3)
Step 2: Distribute the -2
Next, we distribute the -2 to the terms within the second set of parentheses:
10x² - 4x + 15x - 6 - 10x² - 10x + 6x + 6
Step 3: Combine Like Terms
Finally, we combine the like terms to simplify the expression:
**10x² - 10x² - 4x + 15x - 10x + 6x - 6 + 6 = ** 7x
Conclusion
Therefore, the simplified form of the expression (2x+3)(5x-2)-2(5x-3)(x+1) is 7x.