The FOIL method incorporates a useful mnemonic device when conducting mathematical operations using polynomials, which are a combination of number and letter variables. The distributive property is key when trying to multiply by using the FOIL method. FOIL stands for the following: "first, outside, inside, last." And the mathematical set-up in which to use the FOIL method follows the pattern found in the following: EXAMPLE (3x-2)(6x+4).
Instructions
1. Multiply the first 2 sets of terms inside of each parenthesis. These are the terms that come before the operation signs of addition or subtraction. If the terms are both accompanied by letters, such as an x, then add the exponents together. There is an understood exponent of 1 on every term. EX. 3x*6x=18x2
2. Take the "outside" terms, or in other words, the first term in the first parenthesis and the second term in the second parenthesis, and multiply them together. To decide whether a resulting number will be positive or negative goes as follows: the result when a positive number is multiplied by a positive number is a positive number, the result when a positive is multiplied by a negative is a negative, and when a negative is multiplied by a negative the result is a positive number. EX.3x*4=12x
3. Do multiplication on the "inside" terms, or in other words the second term in the first parenthesis and the first number in the second parenthesis. EX. -2*6x=-12x
4. Use the "last" terms, or the second terms in each of the parenthesis, to do the final bit of multiplying. EX. -2*4=-8.
5. Add terms that are alike together, if there are any. That means wherever you see the same letter used in conjunction with various numbers, combine them. Example: 23x and 25x are like terms while 18x and 22b are not. Also, if a letter is squared, cubed, or has other exponents, those terms must be added to only other like squared, cubed, or exponent-having terms. Example: 18x and 18x3 cannot be added together but 18x3 and 2x3 can be added together.
6. Combine the like terms +12x and -12x resulting from the example problem after performing the steps of the FOIL method. The positive and negative of the same number cancels itself out when they are added each other. The final solution to the EXAMPLE is: 18x2-8.
Tags: FOIL method, positive number, added together, each parenthesis, first parenthesis