(m-6)(m^2+6m-7)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (m-6)(m^2+6m-7)

This expression represents the product of two factors: (m-6) and (m^2+6m-7). To expand it, we'll use the distributive property. This involves multiplying each term in the first factor by each term in the second factor and then combining like terms.

Here's how it breaks down:

1. Distribute the 'm' from the first factor:

   • m * (m^2 + 6m - 7) = m^3 + 6m^2 - 7m

2. Distribute the '-6' from the first factor:

   • -6 * (m^2 + 6m - 7) = -6m^2 - 36m + 42

3. Combine the results from steps 1 and 2:

   • m^3 + 6m^2 - 7m - 6m^2 - 36m + 42

4. Combine like terms:

   • m^3 - 43m + 42

Therefore, the expanded form of (m-6)(m^2+6m-7) is m^3 - 43m + 42.

Key Takeaways

• The distributive property is a fundamental tool for expanding algebraic expressions.
• Expanding an expression allows you to simplify it and make it easier to work with in other calculations.
• Pay close attention to signs (positive and negative) when distributing.