Expanding and Simplifying the Expression: (m+5)(m+4)(m-1)
This expression involves multiplying three binomials. We can simplify it by using the distributive property and combining like terms. Here's how to break down the process:
Step 1: Multiply the first two binomials.
(m+5)(m+4)
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FOIL method:
- First: m * m = m²
- Outer: m * 4 = 4m
- Inner: 5 * m = 5m
- Last: 5 * 4 = 20
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Combine like terms: m² + 4m + 5m + 20 = m² + 9m + 20
Step 2: Multiply the result from step 1 with the remaining binomial.
(m² + 9m + 20)(m-1)
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Distributive property:
- m² * (m-1) = m³ - m²
- 9m * (m-1) = 9m² - 9m
- 20 * (m-1) = 20m - 20
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Combine like terms: m³ - m² + 9m² - 9m + 20m - 20 = m³ + 8m² + 11m - 20
Final Result:
Therefore, the simplified form of the expression (m+5)(m+4)(m-1) is m³ + 8m² + 11m - 20.