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

Jasonbradley

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Jun 16, 2024

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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.