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

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (2x-3)(-2x^2-5x-8)

This article will guide you through the process of expanding the expression (2x-3)(-2x^2-5x-8). We will utilize the distributive property to achieve this.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Mathematically, this can be expressed as:

a(b + c) = ab + ac

Expanding the Expression

1. Distribute the first term of the first factor: We begin by distributing the 2x from the first factor to each term in the second factor:

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

2. Distribute the second term of the first factor: Next, we distribute the -3 from the first factor to each term in the second factor:

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

3. Combine the results: Combining the terms we get:

   -4x^3 - 10x^2 - 16x + 6x^2 + 15x + 24

4. Simplify by combining like terms: Finally, we simplify the expression by combining like terms:

   -4x^3 - 4x^2 - x + 24

Conclusion

By using the distributive property, we have expanded the expression (2x-3)(-2x^2-5x-8) into the simplified form -4x^3 - 4x^2 - x + 24. This expanded form provides a more detailed representation of the expression, allowing for further analysis and manipulation.