(-x-3)(2x^2+5x+8)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (-x - 3)(2x² + 5x + 8)

This article will guide you through the process of expanding the given expression: (-x - 3)(2x² + 5x + 8).

Understanding the Process

Expanding this expression means multiplying each term in the first set of parentheses with every term in the second set of parentheses. This is an application of the distributive property.

The Steps

1. Distribute the first term of the first set of parentheses:

   • (-x) * (2x²) = -2x³
   • (-x) * (5x) = -5x²
   • (-x) * (8) = -8x

2. Distribute the second term of the first set of parentheses:

   • (-3) * (2x²) = -6x²
   • (-3) * (5x) = -15x
   • (-3) * (8) = -24

3. Combine like terms:

   • -2x³ - 5x² - 8x - 6x² - 15x - 24

4. Simplify:

   • -2x³ - 11x² - 23x - 24

Conclusion

Therefore, the expanded form of the expression (-x - 3)(2x² + 5x + 8) is -2x³ - 11x² - 23x - 24.