Understanding the FOIL Method: A StepbyStep Guide for (x+3)(x4)
The FOIL method is a helpful mnemonic for remembering how to multiply two binomials. It stands for First, Outer, Inner, Last, representing the order in which you multiply the terms. Let's apply this method to the expression (x+3)(x4).
Breaking Down the FOIL Method

First: Multiply the first terms of each binomial: x * x = x²

Outer: Multiply the outer terms of the binomials: x * 4 = 4x

Inner: Multiply the inner terms of the binomials: 3 * x = 3x

Last: Multiply the last terms of the binomials: 3 * 4 = 12
Combining the Terms
Now we have: x²  4x + 3x  12
Simplifying the Expression
Finally, combine the like terms: x²  x  12
Therefore, the product of (x+3)(x4) using the FOIL method is x²  x  12.
Why the FOIL Method Works
The FOIL method essentially ensures that each term in the first binomial is multiplied by each term in the second binomial. This ensures that all possible combinations are included in the final result.
Conclusion
The FOIL method is a simple yet effective technique for multiplying binomials. By following the steps, you can accurately and efficiently find the product of any two binomials. It's a valuable tool for anyone working with algebraic expressions.