Multiplying Binomials

Binomials are irreducible parts of polynomials.  In this sense they are linear and have a constant term added or subtracted from a single variable with a power of 1.

Example:

(x+2);  (x-3)

[Note that here there is a single variable with power of 1 and a constant term being added or subtracted from it.]

To multiply two monomials, one can use (1) FOIL and (2) Distributive Property

(1) FOIL [First Inner Outer Last]

Example: (x+2)(x-3)= (x)(x)[First]+(x)(-3)[Outer]+(2)(x)[Inner]+(2)(-3)[Last]
                                = x+-3x+2x-6
                                = x-x-6

(2) Distributive Property:

Example: (x+2)(x-3)=(x+2)[x]+(x+2)[-3]
                                =(x[x]+2[x])+(x[-3]+2[-3])
                                =x+2x-3x-6
                                =x-x-6

You see that both methods achieve the same thing, It is simply a matter of preference.  While the brevity of the first may be appealing to most, the second is less arduous with regards to memory and comes more naturally from a mathematical standpoint.