(3x-2)(x+1)-(2x+5)(x^2-1) (x+1)

2 min read Jun 16, 2024
(3x-2)(x+1)-(2x+5)(x^2-1) (x+1)

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

This problem involves simplifying an algebraic expression with multiple terms and parentheses. We can accomplish this by applying the distributive property and combining like terms.

Step 1: Expanding the Products

Let's start by expanding the products using the distributive property (FOIL method):

  • (3x-2)(x+1):

    • 3x * x = 3x²
    • 3x * 1 = 3x
    • -2 * x = -2x
    • -2 * 1 = -2
    • Therefore, (3x-2)(x+1) = 3x² + x - 2
  • (2x+5)(x²-1):

    • 2x * x² = 2x³
    • 2x * -1 = -2x
    • 5 * x² = 5x²
    • 5 * -1 = -5
    • Therefore, (2x+5)(x²-1) = 2x³ + 5x² - 2x - 5

Step 2: Combining Terms

Now, let's substitute the expanded forms back into the original expression:

(3x² + x - 2) - (2x³ + 5x² - 2x - 5)(x+1)

We can simplify this further by distributing the negative sign and then combining like terms:

(3x² + x - 2) - (2x⁴ + 5x³ - 2x² - 5x + 2x³ + 5x² - 2x - 5)

(3x² + x - 2) - (2x⁴ + 7x³ + 3x² - 7x - 5)

-2x⁴ - 7x³ + 7x + 3

Final Result

The simplified form of the expression (3x-2)(x+1)-(2x+5)(x^2-1) (x+1) is -2x⁴ - 7x³ + 7x + 3.

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