FOIL (or F.O.I.L.) is an acronym for "FIRSTS, "OUTERS", "INNERS", "LASTS".

When you have two parentheses multiplied with two terms in each,
like this:

(A + B)(C + D)

(A + B)(C + D)

A and the C are the FIRST terms in each parentheses

You multiply them together and in this case you get AC

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(A + B)(C + D)

The A and the D are the OUTER ones in each parentheses (the furthest apart)

You multiply them together and in this case you get AD

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(A + B)(C + D)

The B and the C are the INNER ones in each parentheses (the closest ones together)

You multiply them together and in this case you get BC

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(A + B)(C + D)

The B and the D are the LAST ones in each parentheses

You multiply them together and in this case you get BD

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So the sum of all four of them is F + O + I + L or

AC + AD + BC + BD

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Edwin