I am unable to simplify a large expression using one given condition.

For example, suppose, I want to simplify the expression 

A=(20*a40*b10^2*b20 - 6*a50*b10^3)*a01^3 + ((-10*a11*a40 + 36*a21*a30)*b10^3 + (7*a11*a30*b20 - 30*a20^2*b21 - 9*a20*a30*b11)*b10^2 + (-12*a11*a20*b20^2 + 39*a20^2*b11*b20)*b10 + 15*b20^2*a11*a20*b11)*a01^2 + (-2*a11^2*a30*b10^3 + (27*a11^2*a20*b20 + 9*a11*a20^2*b11)*b10^2)*a01 + 18*a11^3*a20*b10^3

where it is given that a01*(a20*b20-a30*b10)+a11*a20*b11=0

Is there any way out to simplify A by reducing the number of terms in A? 

I need a proper solution. 

Is there any method to handle the huge expression of A where it is given that sigma+x=a, sigma*x=b

It is huge. I tryed with

B := mtaylor(A, [sigma, x], 8)

Unable to handle. I know that the expression can be written in powers in sigma^ix^j and thereafter sigma+x=a, sigma*x=b could be substituted..

Any help.

Download 1.mw1.mw

How to write a_{01} in Maple

a[01] makes a_1. It mates a[01] - a[1] =0. However, a[0] becomes a_0. What to do? I want to write in maple in such that LaTeX conversion works good.

For a single variable function, I can expand the function 

series(x/(1−x−x^2),x,4);

and get the expansion upto order 4 term.

What shall I do if the function is two variable like f(x,y)=xy/(y−x*sqrt(y)−x^2) and intended to keep terms upto order 5, or moreseries.mw

Download series.mw

say.

My attempt failed as (x^7 + x^5 + x^3 + x)*y etc contains O(8) terms x^7.y

Please help. 

how to write 

-a2/3 + a3 - (2*a4)/3 - (2*a5)/3

into the form 

-(-3*a3 + a2 + 2*a4 + 2*a5)/2

No simplify works. Please help.