(x2-3x+2)(5x-2)-(3x2+4x-5)(2x-1)

2 min read Jun 17, 2024

Simplifying the Expression: (x²-3x+2)(5x-2) - (3x²+4x-5)(2x-1)

This article will guide you through simplifying the algebraic expression: (x²-3x+2)(5x-2) - (3x²+4x-5)(2x-1). We will use the distributive property and combine like terms to reach a simplified form.

Step 1: Expanding the Products

First, we need to expand the products using the distributive property (also known as FOIL).

For the first product: (x²-3x+2)(5x-2)
- Multiply each term in the first parenthesis by each term in the second:
- (x² * 5x) + (x² * -2) + (-3x * 5x) + (-3x * -2) + (2 * 5x) + (2 * -2)
- Simplifying: 5x³ - 2x² - 15x² + 6x + 10x - 4
For the second product: (3x²+4x-5)(2x-1)
- Multiply each term in the first parenthesis by each term in the second:
- (3x² * 2x) + (3x² * -1) + (4x * 2x) + (4x * -1) + (-5 * 2x) + (-5 * -1)
- Simplifying: 6x³ - 3x² + 8x² - 4x - 10x + 5

Step 2: Combining Like Terms

Now we have: (5x³ - 2x² - 15x² + 6x + 10x - 4) - (6x³ - 3x² + 8x² - 4x - 10x + 5)

Let's combine like terms within each parenthesis:

First parenthesis: 5x³ - 17x² + 16x - 4
Second parenthesis: 6x³ + 5x² - 14x + 5

Step 3: Subtracting the Second Parenthesis

Remember to distribute the negative sign to all terms in the second parenthesis:

5x³ - 17x² + 16x - 4 - 6x³ - 5x² + 14x - 5

Step 4: Final Simplification

Combine like terms to get the final simplified expression:

-x³ - 22x² + 30x - 9

This is the simplified form of the original expression.