How to Use Combinations to Expand Binomial Expressions

When solving difficult math problems, using mnemonic devices can be useful in remembering how to solve equations. In mathematical binomial equations, the FOIL method stands for First, Outer, Inner, Last: this refers to the order in which you solve the equation. Once you have used the FOIL method, you will combine like elements of the equation to solve for the final solution.

Instructions

1. Use the FOIL method to expand the equation. For example:

   (3z + 5) x (2z + 7)

   Multiply the first parts of the equation, 3z x 2z, to get 6z^2. Then multiply the outer parts of the equation, 3z x 7, to get 21z. Next take the inner parts, 5 x 2z, to get 10z. Finally, take the last parts of the equation, 5 x 7, to get 35.

2. Write out the remaining expanded binomial. It will look like this:

   6z^2 + 21z + 10z +35

3. Combine the like elements in the expanded binomial equation. It will look like this:

   6z^2 + 31z + 35

References

• Algebra.help: Simplifying Using the FOIL Method