(2x-5)-11x(x-2)%2B5(x%5E2-3x-1).jpeg "(3x+4)(2x-5)-11x(x-2)+5(x^2-3x-1)")
Simplifying the Expression: (3x+4)(2x-5)-11x(x-2)+5(x^2-3x-1)
This article will guide you through the process of simplifying the given algebraic expression: (3x+4)(2x-5)-11x(x-2)+5(x^2-3x-1).
Step 1: Expand the products
We'll start by expanding each of the products in the expression:
- (3x+4)(2x-5) : Using the FOIL method (First, Outer, Inner, Last), we get: (3x * 2x) + (3x * -5) + (4 * 2x) + (4 * -5) = 6x² - 15x + 8x - 20 = 6x² - 7x - 20
- -11x(x-2) : Distributing -11x gives us: -11x² + 22x
- 5(x²-3x-1) : Distributing 5 gives us: 5x² - 15x - 5
Step 2: Combine like terms
Now, let's combine the terms that have the same variable and exponent:
(6x² - 7x - 20) + (-11x² + 22x) + (5x² - 15x - 5)
Combining x² terms: 6x² - 11x² + 5x² = 0x² Combining x terms: -7x + 22x - 15x = 0x Combining constant terms: -20 - 5 = -25
Step 3: The Simplified Expression
After combining all like terms, the simplified expression becomes:
0x² + 0x - 25 = -25
Therefore, the simplified form of the expression (3x+4)(2x-5)-11x(x-2)+5(x^2-3x-1) is -25. This means the expression is a constant value, regardless of the value of 'x'.