by LoveMath on Mon Sep 03, 2012 5:02 am
To answer where the B term came from in the expression ax^2+bx+c, are you familiar with the foil method of multipying a binomial by a binomial? If not, it's an acronymn that stands for First, Outer, Inner, Last.
First: multilipy each of the first terms in both parentheses. This gives you (4x)(2x) = 8x^2
Outer: multiply each of the outermost terms in both parentheses. These are: (4x)(+3) = +12x
Inner: multiply each of the innermost terms in both parentheses. These are (-3)(2x) = -6x
Last: multiply each of the last (or second) terms in both parentheses. These are: (-3)(+3) = -9
Then if you combine the outer and inner terms of +12x and -6x you will get +6x.
And this is where the middle term comes from.
You might be able to visualize this concept by putting your hands by the 2 outer terms, multiply them and here we got +12x.
Then place your hands in the center by the two innermost terms, multiply them and you get -6x.
I generally just repeat this process several times to students...outer, inner....then add the two.
Make sense?