(7u^2+8uv-6v^2)(6u^2+4uv+3v^2)

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials: (7u^2+8uv-6v^2)(6u^2+4uv+3v^2)

This problem involves multiplying two trinomials. To do this, we'll use the distributive property (often referred to as FOIL for binomials) multiple times.

Here's the breakdown:

1. Distribute the first term of the first trinomial:

   • (7u^2)(6u^2+4uv+3v^2) = 42u^4 + 28u^3v + 21u^2v^2

2. Distribute the second term of the first trinomial:

   • (8uv)(6u^2+4uv+3v^2) = 48u^3v + 32u^2v^2 + 24uv^3

3. Distribute the third term of the first trinomial:

   • (-6v^2)(6u^2+4uv+3v^2) = -36u^2v^2 - 24uv^3 - 18v^4

4. Combine like terms:

   • 42u^4 + 28u^3v + 21u^2v^2 + 48u^3v + 32u^2v^2 + 24uv^3 - 36u^2v^2 - 24uv^3 - 18v^4

5. Simplify:

   • 42u^4 + 76u^3v + 17u^2v^2 - 18v^4

Therefore, the product of (7u^2+8uv-6v^2)(6u^2+4uv+3v^2) is 42u^4 + 76u^3v + 17u^2v^2 - 18v^4.

Key points to remember:

• FOIL (First, Outer, Inner, Last) is a helpful mnemonic for multiplying binomials, but it doesn't apply directly to trinomials.
• Organization: Write out each step clearly, making sure to distribute correctly and combine like terms.
• Practice: Practice multiplying binomials and trinomials to become more familiar with the process.