How to Multiply Binomials Using Foil
As a student travels through the world of math you will run into multiplying binomials. The binomials we will use for this are: (X+4) and (X+3). You can not move further without this crucial skill. The best way to multiply binomials is to use a method named FOIL. This is not only the name, but also a handy way of remembering how to do it. Once you master this skill, the rest of Algebra will unravel for you like a ball of aluminum FOIL.
- Difficulty:
- Moderately Easy
Instructions
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multiply binomials with foil
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1
F - The first step of FOIL.
Set up our binomials as a multiplication problem. (X+4)(X+3) FOIL is the name of the procedure as well as the steps to perform the multiplication. Now we start with F - which means to multiply the First two numbers(letters) of each binomial together. This will give you the first number of the answer. X times X = X squared or X with a raised 2. (our first number) Your answer now looks like this: X(squared) +
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2
Continue to the next part of FOIL, "O". However, "O" and "I" are the only letters in the Algebra universe that work together. Therefore, "O" will be one part of the 2nd number of the answer. O-which means to multiply the Outer most items of the binomials together. X times 3 = 3x(our outer number) Now that you have the number 3x, set it aside and move on to I. Your answer now looks like this: X(squared) + (3X +
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3
Multiply the inner numbers together. This where "I" and "O" come together to help each other out. I-which means to multiply the inner numbers together. 4 times X = 4x(our inner number)Your answer now looks like this: X(squared) + (3x+4x) + You must now add "I" and "O" together changing the answer to: X(squared + 7x +
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4
Multiply the last numbers of the binomial. The final letter in FOIL is L. L-which means last. The last numbers in our example is a 4 and a 3. 4 X 3=12(our last number) Therefore our answer is the polynomial X(squared) + 7x + 12. So (X+4)(X+3) = X(squared) +7x+12
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1
Tips & Warnings
When working with FOIL, never try to go to quickly. It is very easy to make a mistake, and when that happens the entire equation falls apart very quickly.
Remember, add inner and outer together to get the middle number
When you are multiplying a negative number and a positive number you will get a negative number
When multiplying two negative numbers you will get a positive number
When adding two negative numbers, you will get an even bigger negative number.
