# Binomials!

Binomials, as discusses earlier, are pairings of a Variable and a Constant, such as (3X+7). When dealing with binomials, you have to keep them together, meaning if you were to divide (2X+4) by 2, you would have to divide both the (2X) and the (4) by 2, and the result would be (X+2).

### Addition and Subtraction of Binomials

When adding or subtrating binomials, all you have to do is combine like terms, the X's with the X's, and the numbers with the numbers. Meaning; (3X+7) + (2X+3) = ((3X+2X)+(7+3)) = (5X+10). And when subtracting; (9X+17) - (3X+12) = ( (9X-3X) + (17-12) ) = (6X+5). Even with negatives it works the same way, so: (6X+(-3)) = (6X-3). (6X-3) + (2X+5) = ( (6X+2X) + ((-3)+5) )=(8X+2).

### Multiplication of Binomials

In order to multiply two binomials, you would use a method called FOIL. This stands for First, Outer, Inner, Last. These four words represent the different multiplications between the two binomials that must occur for you to find the resultant.   For example, doing (X+3)*(2X+1)

• First: Multiply the first term in each binomial (the terms with the "X" in it). (X)*(2X)
• Outer: Multiply the outer two terms of the binomials (X)*(1)
• Inner: Multiply the inner two terms of the binomials (3)*(2X)
• Last: Multiply the last term of each binomial (the constant terms). (3)*(1)
Now you would add together each term to find out what would result. (X*2X)+(X*1)+(3*2X))+(3*1) = (2X2)+(6X)+(X)+(3) = 2X2+7X+3.
Binomials MUST be kept together!