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Expanding the Expression (m+2)(m+5)
This article will guide you through the process of expanding the algebraic expression (m+2)(m+5). This type of expression is called a binomial multiplication, where we multiply two binomials (expressions with two terms).
The FOIL Method
To expand (m+2)(m+5), we can use the FOIL method. FOIL stands for First, Outer, Inner, Last. It's a systematic way to ensure we multiply each term in the first binomial by each term in the second binomial.
Here's how it works:
- First: Multiply the first terms of each binomial: m * m = m²
- Outer: Multiply the outer terms of the binomials: m * 5 = 5m
- Inner: Multiply the inner terms of the binomials: 2 * m = 2m
- Last: Multiply the last terms of the binomials: 2 * 5 = 10
Combining Like Terms
Now, we have the expression: m² + 5m + 2m + 10
Notice that 5m and 2m are like terms (they have the same variable and exponent). We can combine them:
m² + 5m + 2m + 10 = m² + 7m + 10
Conclusion
Therefore, the expanded form of (m+2)(m+5) is m² + 7m + 10.
This method can be applied to any binomial multiplication. Remember to multiply each term in the first binomial by each term in the second binomial, and then simplify by combining like terms.