You use the FOIL method when you are multiplying two binomials; that is multiplying two factors with two terms in each factor.
The FOIL method lets you multiply two binomials in a particular order. You don’t have to multiply binomials by following the FOIL order, but it does make the process easier. The letters in FOIL refer to two terms (one from each of two binomials) multiplied together in a certain order: First, Outer, Inner, and Last.
Outside terms are multiplied next: q * (−7) = −7q. Inside terms are multiplied next: −3 * q = −3q. Last, multiply last terms of each binomial: −3 * (−7) = 21.
The foil method is an effective technique because we can use it to manipulate numbers, regardless of how they might look ugly with fractions and negative signs.
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.
A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.
To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.
The FOIL Method always works for factoring trinomials and is a very helpful tool if you can’t wrap your brain around guess-and-check. When the FOIL method fails, you know for certain the given quadratic is prime. The FOIL method of factoring calls for you to follow the steps required to FOIL binomials, only backward.
foil, in literature, a character who is presented as a contrast to a second character so as to point to or show to advantage some aspect of the second character. … Watson is a perfect foil for Holmes because his relative obtuseness makes Holmes’s deductions seem more brilliant.
A literary foil is a character whose purpose is to accentuate or draw attention to the qualities of another character, most often the protagonist.
The problem, of course, is that the ever-popular FOIL Method only works when multiplying two binomials. … That one is so egregiously harmful: not only does it cause at least as much confusion as it allegedly alleviates, but it makes students helpless in the face of other cases of polynomial multiplication.
Perhaps we can justify the multiplication of binomials as a way to gain sufficient fluency for the time they will be factoring trinomials. Sufficient practice with binomials ahead of time creates familiarity so that when they are factoring they can begin to predict what answers would and should look like.
The FOIL method is used to multiply binomials, or to multiply (x + 3) by (3x -12) for example. Then multiply the OUTSIDE terms together, or x and -12 to get -12x. Then multiply the INSIDE terms together, or 3 and 3x to get 9x. The multiply the LAST terms together, or 3 and -12 to get -36.
When we multiply (x−3) times (x−4) to obtain x2−7x+12 x 2 − 7 x + 12 we call that operation “multiplying out” or sometimes FOILing. (Recall that FOIL stands for First, Outer, Inner, Last, which is how we combine the terms.)