How to Use Foil to Distribute Two Binomials

Foil stands for first, outer, inner and last and it refers to how to take two binomials and multiply them together to get a single quadratic equation. Many quadratic expressions like 6X²+7X-3 are the results of multiplying two binomials. Or two terms, separated by addition and subtraction together.

You can undo the multiplication by factoring them but what does foil really stand for? The letters each refer to two terms, one from each of two binomials multiplied together in a certain order. The steps don’t have to be done in this order but they usually are, otherwise the acronym would be something like awful, heaven forbid. Here is what each letter in the foil acronyms stands for.

F stands for the first term in each binomial, in this case the 3A and 2A. O, stands for the two outermost terms. Those farthest to the left and right, the 3A and 1, I stands for the inner terms in the middle. And L stands for the last term in each binomial.

Here is how to use foil on the multiplication problem. First, multiply the first term the F of each binomial together. Second, multiply the outer terms together and third, multiply the inner or I terms together. Fourth, multiply the last term of each expression together and finally list the four results of foil in order.

Now combine the like terms, this example is a bit more complicated. But foil makes it much easier, the task server broken down into smaller, simpler task. And then the results are combined for the final result, here are the steps. Just like before, the first step is to multiply the first terms. Then multiply the outer terms, third multiply the inner terms, fourth multiply the last terms. The last terms are two binomials too, you foil these binomials when finished the series of foils steps.

Fifth, list the four results of foil in order and finally combine like terms. Notice the product of two binomials from step four. You can foil them, this is probably starting to sound familiar. First multiply the first terms, second multiply the outer terms, third multiply the inner terms, fourth multiply the last terms, fifth write the results in order. And then combine the like terms, now replace the two binomials multiplied together with this new result. And you can re-write the entire problem.

This may seem complicated but using foil is actually easier than doing or the distributing. And sticking with the acronym keeps you from accidentally forgetting to multiply one pair of terms.


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