Read this article, which gives many examples of using the FOIL technique to multiply two binomials. Then, try some practice problems.
Recall the the distributive law: for all real numbers, , and , .
At first glance, it might not look like the distributive law applies to the expression
However, it does: once you apply a popular mathematical technique called treat it as a singleton.
Here is how treat it as a singleton goes:
First, rewrite the distributive law using some different variable names: .
This says that anything timesis the anything times , plus the anything times .
Now, look back at, and take the group as .
That is, you are taking something that seems to have two parts, and you are treating it as a single thing, a singleton!
Look what happens:
|Use the distributive law|
|Use the distributive law twice|
|Re-order; switch the two middle terms|
You get four terms, and each of these terms is assigned a letter. These letters form the word FOIL, and provide a powerful memory device for multiplying out expressions of the form.
Here is the meaning of each letter in the word FOIL:
One common application of FOIL is to multiply out expressions like
Remember the exponent laws, and be sure to combine like terms whenever possible:
You want to be able to write this down without including the first step above:
Then, after you have practiced a bit, you want to be able to combine the ‘outers’ and ‘inners’ in your head,
and write it down using only one step:
Write your answer in the most conventional way.
Answers must be written in the most conventional way:
term first, term next, constant term last.
For example, type 'x^2' for .
Source: Tree of Math, https://www.onemathematicalcat.org/algebra_book/online_problems/foil_1x.htm
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