(5x-2)-(3x%5E2%2B4x-5)(2x-1).jpeg "(x^2-3x+2)(5x-2)-(3x^2+4x-5)(2x-1)")
Expanding and Simplifying the Expression: (x^2-3x+2)(5x-2)-(3x^2+4x-5)(2x-1)
This problem involves expanding and simplifying a complex algebraic expression. Let's break it down step by step:
1. Expanding the Products:
We'll use the distributive property (also known as FOIL) to expand each of the products:
- First Product: (x^2-3x+2)(5x-2)
- (x^2 * 5x) + (x^2 * -2) + (-3x * 5x) + (-3x * -2) + (2 * 5x) + (2 * -2)
- 5x^3 - 2x^2 - 15x^2 + 6x + 10x - 4
- Second Product: (3x^2+4x-5)(2x-1)
- (3x^2 * 2x) + (3x^2 * -1) + (4x * 2x) + (4x * -1) + (-5 * 2x) + (-5 * -1)
- 6x^3 - 3x^2 + 8x^2 - 4x - 10x + 5
2. Combining Like Terms:
Now, we combine the terms from both expanded products:
(5x^3 - 2x^2 - 15x^2 + 6x + 10x - 4) - (6x^3 - 3x^2 + 8x^2 - 4x - 10x + 5)
- x^3 Terms: 5x^3 - 6x^3 = -x^3
- x^2 Terms: -2x^2 - 15x^2 + 3x^2 - 8x^2 = -22x^2
- x Terms: 6x + 10x + 4x + 10x = 30x
- Constant Terms: -4 - 5 = -9
3. Simplified Expression:
Combining all the terms, we get the simplified expression:
-x^3 - 22x^2 + 30x - 9
Therefore, the simplified form of the expression (x^2-3x+2)(5x-2)-(3x^2+4x-5)(2x-1) is -x^3 - 22x^2 + 30x - 9.