kill(all)$

van=facebook.com/LearningCalculus$

     Generalized Polynomial Representation

P(a,u,k):=block([expr],expr:a[0],for i: 1 thru k do expr:expr+a[i]*u^i,expr)$

P(b,x,4)*P(a,y,3)*P(c,z,2);

     Sums and Differences of polynomials produce no new shape.

P(a,x,4)+P(b,x,4);

collectterms(%,x);

collectterms(P(a,x,4)-P(b,x,4),x);

collectterms(expand(P(a,x,2)*P(b,x,2)),x);

     Rational forms lead to curves with
     fundamentally different properties.

P(a,x,4)/P(b,x,5);