What is the Foil Method?
Multiplying Terms Using the Foil Method
The most common method for multiplying a pair of two-termed expressions is called the FOIL method. FOIL stands for First, Outside, Inside, and Last, and describes the order in which you multiply each pair of terms. You would multiply the first pair, the outside pair, the inside pair, and then the last pair.
That’s the order in which we’ll proceed here. First pair is going to be 3x times 4x, which gives us 12x squared. The outside pair is 3x times -2, which gives us minus 6x. The inside pair 6 times 4x gives us 24x, and the last pair 6 times -2 gives us minus 12. We need to combine like terms. We have 2 x’s here, so we’ll go ahead and combine those.
That gives us 12x squared plus 18x minus 12. Now, each of these numbers is a multiple of 6, so we can pull a 6 outside of this expression. That gives us 2x squared plus 3x minus 2. In the second example here, we have a three-termed expression and a two-termed expression. We can’t use—we can’t strictly use the FOIL method, but we use an extrapolation of the FOIL method.
The FOIL method takes the first term in the first expression and multiplies it in order by each of the terms in the second expression, then moves onto the second term the first expression and multiplies it by each of the terms in the second expression.
To extrapolate that to a three-termed expression, we’ll start with the first term, move to the second term, and then move to the third term. The first in order is going to be x squared times 3x. That gives us 3x cubed. X squared times -4 gives us -4x squared.
Moving to the second term here, minus 2x times 3x gives us minus 6x squared. Minus 2x times minus 4 equals plus 8x. Moving on to the third term here, 1 times 3x is 3x, and 1 times -4 is -4. Once again, we need to combine like terms.
We have a pair of x squareds and a pair of x’s. We’ll go ahead and combine those. We have 3x cubed minus 4x squared minus 6x squared gives us a minus 10x squared plus 8x plus 3x gives us a plus 11x and we still have a -4.