(n%2B3)-foil-method.jpeg "(3n+2)(n+3) Foil Method")
FOIL Method: Expanding (3n+2)(n+3)
The FOIL method is a mnemonic acronym for a common method used to multiply two binomials. It stands for First, Outer, Inner, Last, representing the order in which you multiply the terms of the binomials.
Let's apply the FOIL method to expand the expression (3n + 2)(n + 3):
1. First: Multiply the first terms of each binomial:
- (3n) * (n) = 3n²
2. Outer: Multiply the outer terms of the binomials:
- (3n) * (3) = 9n
3. Inner: Multiply the inner terms of the binomials:
- (2) * (n) = 2n
4. Last: Multiply the last terms of each binomial:
- (2) * (3) = 6
Now, combine all the terms: 3n² + 9n + 2n + 6
Finally, simplify by combining like terms: 3n² + 11n + 6
Therefore, the expanded form of (3n + 2)(n + 3) using the FOIL method is 3n² + 11n + 6.
Key Takeaways:
- The FOIL method is a simple and systematic way to multiply binomials.
- It ensures that all possible combinations of terms are considered.
- Remember to combine like terms after multiplying to obtain the final simplified expression.