(x%2B1)-3x(x%5E2-x-3)-2x(x-5)(x-4).jpeg "(5x-2)(x+1)-3x(x^2-x-3)-2x(x-5)(x-4)")
Simplifying the Expression (5x-2)(x+1)-3x(x^2-x-3)-2x(x-5)(x-4)
This article aims to break down the process of simplifying the given algebraic expression: (5x-2)(x+1)-3x(x^2-x-3)-2x(x-5)(x-4).
Step 1: Expanding the Products
We begin by expanding each product in the expression:
- (5x-2)(x+1): This is a simple binomial multiplication.
- (5x-2)(x+1) = 5x² + 5x - 2x - 2
- = 5x² + 3x - 2
- 3x(x²-x-3): Here, we distribute the 3x to each term inside the parentheses.
- 3x(x²-x-3) = 3x³ - 3x² - 9x
- 2x(x-5)(x-4): We can use the distributive property twice. First, we multiply the first two terms, and then multiply the result by the remaining term.
- 2x(x-5)(x-4) = 2x(x²-9x + 20)
- = 2x³ - 18x² + 40x
Step 2: Combining Like Terms
Now, let's rewrite the entire expression with the expanded terms:
5x² + 3x - 2 - 3x³ + 3x² + 9x - 2x³ + 18x² - 40x
Next, we combine the terms with the same variable and exponent:
- -3x³ - 2x³ = -5x³
- 5x² + 3x² + 18x² = 26x²
- 3x + 9x - 40x = -28x
Step 3: Final Result
Putting it all together, the simplified form of the expression is:
-5x³ + 26x² - 28x - 2
Therefore, the simplified expression is -5x³ + 26x² - 28x - 2.