(-3m^2-2mn-8n^2)(8m^2+4mn+n^2)

Jasonbradley

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Jun 16, 2024

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Multiplying Trinomials: A Step-by-Step Guide

This article will guide you through the process of multiplying the trinomials (-3m^2-2mn-8n^2) and (8m^2+4mn+n^2).

Understanding the Process

Multiplying trinomials is similar to multiplying binomials, but with an extra term. We can use the distributive property or the FOIL method (First, Outer, Inner, Last) to simplify the expression.

Step-by-Step Solution

1. Distribute the first term of the first trinomial:

   • (-3m^2) * (8m^2+4mn+n^2) = -24m^4 - 12m^3n - 3m^2n^2

2. Distribute the second term of the first trinomial:

   • (-2mn) * (8m^2+4mn+n^2) = -16m^3n - 8m^2n^2 - 2mn^3

3. Distribute the third term of the first trinomial:

   • (-8n^2) * (8m^2+4mn+n^2) = -64m^2n^2 - 32mn^3 - 8n^4

4. Combine all the terms:

   • -24m^4 - 12m^3n - 3m^2n^2 - 16m^3n - 8m^2n^2 - 2mn^3 - 64m^2n^2 - 32mn^3 - 8n^4 = -24m^4 - 28m^3n - 75m^2n^2 - 34mn^3 - 8n^4

Final Answer

Therefore, the product of (-3m^2-2mn-8n^2) and (8m^2+4mn+n^2) is -24m^4 - 28m^3n - 75m^2n^2 - 34mn^3 - 8n^4.

Key Takeaways

• Distributive Property: The distributive property is a fundamental concept in algebra, allowing us to multiply expressions by distributing each term.
• Combining Like Terms: Remember to combine like terms after distributing to simplify the final expression.

This method can be applied to multiplying any trinomials, making it a valuable skill in algebra.