The FOIL method is a way to multiply two different sets of two-term polynomials. FOIL is an acronym for “first,” “outer,” “inner” and “last,” all of which refer to the order in which students should multiply the numerals of each pair. This method can be used in fourth grade math to multiply two two-digit numbers, though the numbers in question must first be broken down into polynomials. With a little practice, fourth grade students should be able to memorize and employ the FOIL method whenever needed.

First

If you’re using the FOIL method to multiply two two-digit numbers, the first thing you’ll need to do is convert each of those numbers into polynomials/expanded notation. For example, if you are multiplying 22 and 44, you'd expand 22 into (20 + 2) and 44 into (40 + 4). Now that you have two sets of polynomials, you can proceed with the FOIL method. First, multiply the “first” numbers in each set. In this case, the first numbers of each set are 20 and 40, respectively. When multiplied together, these numbers become 800. Make sure to write down this answer, as you’ll be adding it together with the answers of the next three parts of the FOIL technique.

Outer

Once you’ve gotten an answer for the “first” numbers, it’s time to solve the “outer” section of the equation. In the case of the problem (20 + 2) (40 + 4), the outer numbers would be the numbers farthest apart from each other: 20 and 4. Multiplied together, they become 80. Write this number down next to your answer for the previous section, so that you end up with 800 + 80.

Inner

The next step in the FOIL technique is “inner.” These are the numbers that are physically closest to each other. In the case of the example (20 + 2) (40 + 4), the inner numbers are 2 and 40. Multiply these numbers together to get 80. Add this new number to your growing list of FOIL products, so that you have the following set of numbers: 800 + 80 + 80.

Last

Now that you’ve found products for the first, outer and inner numbers of your polynomial pair, it’s time to multiply the “last” numbers in each set. The last numbers are whatever numbers appear farthest to the right in each pair. In the case of (20 + 2) (40 + 4), the last numbers are 2 and 4. Multiplied together, these numbers become 8. Add this number to your other FOIL answers, so that you have the numerals: 800 + 80 + 80 + 8.

Final FOIL Step

Now that you have answers for each section of the FOIL technique, it’s time to add them up. The sum of 800 + 80 + 80 + 8 is 968. To check your work, you can go back to the original multiplication problem and find the answer with a calculator, which confirms that 22 x 44 = 968.

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