Multiplying Binomials
binomials, polynomials, foil, distributive property, irreducible, linear, constant, power, single variable
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
2+-3x+2x-6
= x
2-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
2+2x-3x-6
=x
2-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.
binomials, polynomials, foil, distributive property, irreducible, linear, constant, power, single variable