Symbolic Math - A Workflow

Hey, knock yourself out, but Sage (http://www.sagemath.org/) integrates, and improved on, Maxima, and represents a much more advanced free tool for symbolic mathematics.

Also, there's Sympy (http://sympy.org/en/index.html), a Python library that does symbolic mathematics and would be a much better and simpler way for you to explain and demonstrate symbolic mathematics in a tutorial. Let's use Sympy to solve a quadratic:

    from sympy import *
    var('x a b c')
    sol = solve(a * x**2 + b * x + c,x)
    print(sol)
    print(latex(sol))

    [(-b + (-4*a*c + b**2)**(1/2))/(2*a), -(b + (-4*a*c + b**2)**(1/2))/(2*a)]