(m-2n).jpeg "(4m+n)(m-2n)")
Expanding the Expression (4m + n)(m - 2n)
In mathematics, expanding an expression involves simplifying it by removing parentheses and combining like terms. The expression (4m + n)(m - 2n) is a product of two binomials and can be expanded using the FOIL method.
What is the FOIL Method?
FOIL stands for First, Outer, Inner, Last. It's a mnemonic device that helps remember the steps involved in expanding the product of two binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding (4m + n)(m - 2n)
Let's apply the FOIL method to our expression:
- First: (4m)(m) = 4m²
- Outer: (4m)(-2n) = -8mn
- Inner: (n)(m) = mn
- Last: (n)(-2n) = -2n²
Now, combine the resulting terms:
4m² - 8mn + mn - 2n²
Finally, simplify by combining the 'mn' terms:
4m² - 7mn - 2n²
Conclusion
By using the FOIL method, we expanded the expression (4m + n)(m - 2n) to obtain the simplified form 4m² - 7mn - 2n². This method allows for a systematic and organized way to multiply binomials.