(3x2+5x-7)(x-1)-(x2-2x+3)(x+4)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (3x² + 5x - 7)(x - 1) - (x² - 2x + 3)(x + 4)

This article aims to simplify the given algebraic expression: (3x² + 5x - 7)(x - 1) - (x² - 2x + 3)(x + 4)

To simplify this expression, we will follow these steps:

1. Expand each product using the distributive property (or FOIL method):

   • (3x² + 5x - 7)(x - 1) = 3x³ - 3x² + 5x² - 5x - 7x + 7
   • (x² - 2x + 3)(x + 4) = x³ + 4x² - 2x² - 8x + 3x + 12

2. Combine like terms in each expansion:

   • (3x² + 5x - 7)(x - 1) = 3x³ + 2x² - 12x + 7
   • (x² - 2x + 3)(x + 4) = x³ + 2x² - 5x + 12

3. Substitute the expanded products back into the original expression:

   • (3x³ + 2x² - 12x + 7) - (x³ + 2x² - 5x + 12)

4. Distribute the negative sign:

   • 3x³ + 2x² - 12x + 7 - x³ - 2x² + 5x - 12

5. Combine like terms again:

   • 2x³ - 7x - 5

Therefore, the simplified form of the expression (3x² + 5x - 7)(x - 1) - (x² - 2x + 3)(x + 4) is 2x³ - 7x - 5.