a^nb^2[3b^n-1-2ab^n+1+(-1)^2003]
=a^n*b^2*[3b^(n-1)-2ab^(n+1)-1]
=3a^nb^(n+1)-2a^(n+1)b^(n+3)-a^nb^2
a^n(a^n+1+a^n+a^n-1)-a^n-1(a^n+1+a^n-a^n-1)
=a^(2n+1)+a^2n+a^(2n-1)-a^(2n)-a^(2n-1)+a^(2n-2)
=a^(2n+1)+a^(2n-2)
1/2x(-3x^2+4x+3)-1/3x^2(2x-6x^2)
=-3x^3/2+2x^2+3x/2-2x^3/3+2x^4
=2x^4-13x^3/6+2x^2+3x/2