* MULTIPLICATION OF POLYNOMAILS
** CONTENT
*** MONOMIAL BY MONOMIAL
There are atleast 3-4 steps that you need to follow just to
multiply monomials by monomials, The example that I will be
using is going to be one we will solve

                   (2x^2y) * (6x^3y^2)
                   
STEP 1: Use the commutative Property of Multiplication, and
solve the coefficients first

              (2 * 6)(x^2 y * x^3 y^2)
                     = (12)(x^2 y * x^3 y^2)

STEP 2: Apply the product rule from the laws of exponents
lecture, read L53GPMTH for more information about it.

              (12)(x^2 y * x^3 y^2)
                     = (12)(x^2+3 y^1+2)
                     = (12)(x^5 y^3)

STEP 3: Multiply/Simplify

                    (12x^5y^3)
*** MONOMIAL BY BINOMIAL/TRINOMIAL
This will  be the  example equation that  will be  used for
this lecture notes thing:

                  (-4a^3)(a^2 + 7)

STEP 1:  Apply the  distributive property and  multiply the
coefficients, if  there are  variables, do ignore  them and
just  copy them  after  you  got the  product,  as for  the
exponents, the product rule applies here.

        (-4a^3)(a^2 + 7)
              = (-4a^3 * a^2)(4a^3 * 7)
              = (-4a^5)(28a^3)

This concept applies when it comes to monomials multiplied
to trinomials, 

        (3u^2v^3)(u^2 + v^2 - 5)
             = (3u^2v^3 * u^2) (3u^2v^3 * v^2)
             (3u^2v^3 * -5)

             = (3u^4v^3) + (3u^2v^5) - (15u^2v^3)
             = (3u^4v^3 + 3u^2v^5 - 15u^2v^3)
*** BINOMIAL BY BINOMIAL
Honestly, this  is my  favorite technique, Though  before i
introduce it, I would like to note that there are different
ways of multiplying binomials by  binomials, one of them is
using the  distributive property of multiplication,  but in
this notes file, ill use the FOIL method:

                 F      O      I     L
                 |      |      |     | 
               First  Outer  Inner  Last
               Terms  Terms  Terms  Terms

So how do you use this? well take a look at this equation
and the graphing that i wrote for it
                              
                              L
                         F    |
                         |  _____
                       ____|__   |
                      |    | |   |
                     (x + 2)(x + 3)
                      |   |__|---|--> I  
                      |__________|
                            |   
                            O

I literally wasted 10 minutes arranging this, so you better
appreciate  this  section,  anyways,   what  FOIL  does  is
seperating all  these terms  into four  parts, if  you list
what the graph is trying to identify, you will get this:

             F         O         I         L
          (x * x) + (x * 3) + (2 * x) + (2 * 3)

What do you do with this then? Multiply and simplify them!

               (x^2) + (3x) + (2x) + (6)
             = (x^2) + (5x) + (6)
             = (x^2 + 5x + 6) <--- this is the final answer

And that's how you solve binomials by binomials
            
*** TRINOMIAL BY TRINOMIAL
*** BINOMIAL BY TRINOMIAL