The FOIL Method is used to multiply binomials. is an acronym. The letters stand for First, Outside, Inside, and Last, referring to the order of multiplying terms. You multiply first terms, then outside terms, then inside terms, then last terms, and then combine like terms for your answer.
The mnemonic tells us exactly what terms to multiply, and in what order:
[Insert a large, colorful graphic showing the problem (5n + 3)(n + 6), with identifying arrows and words pointing to the 5n and n as First; the 5n and 6 as Outside; the 3 and n as Inside; and the 3 and 6 as Last]
By following First, Outer, Inner, Last, we do not overlook any term in either binomial. All the terms in the first binomial are combined with the terms in the second binomial properly. Everything gets counted.
Let's apply the method on a couple of examples.
Here we are multiplying two binomials:
Let's go through each step of to solve this multiplication problem:
Put your four answers down on paper in the order you found them:
Finish by combining like terms:
Now, let's use the method on this equation:
Go through each letter:
Put your answers together:
Combine like terms:
Our final answer, the product of two binomials, contains three terms so it is a trinomial.
Multiplying three binomials is a special case for because the method can only be used for multiplying two binomials at a time.
You can use FOIL to multiply three or more binomials if you pair them off, then factor the answer to the remaining binomial.
Here is a multiplication equation with three binomials:
To begin, we pair off the first two binomials:
Then, multiply them using the method, and we get:
Next, we combine like terms:
Now, we multiply our new binomial with the remaining binomial form the original equation:
Then, factoring and simplifying is the final step:
If you are faced with more multiplying two binomials, solve two at a time using until you are left with just one polynomial.
The term polynomial refers to an expression of constants, variables, and exponents that are added, subtracted, or multiplied, like the highlighted answer above. Each term on it's on is called a monomial.
Give these practice problems a try.
Don't foil around with partial work; get answers down on paper before you check our answers.
First, multiply first terms of each binomial:
Outside terms are multiplied next:
Inside terms are multiplied next:
Last, multiply last terms of the binomials:
Now we have:
Combining like terms yields:
After working your way through this lesson and video, you will have learned:
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