How to collect terms of a given type (with subscript and power) in an expression?

Question

Suppose that I have an expression:

expr=(2 λ f[
 z]^3 (λ (Subscript[λ, 0, 2] + 
     Subscript[λ, 2, 0]) - Subscript[λ^2, 0, 1] - 
  Subscript[λ^2, 1, 0]) - λ^2 (Subscript[z^2, 0, 
  1] + Subscript[z^2, 1, 0])^2 Derivative[1][f][z]^2 + f[z]^2 (4 λ^2 (-Subscript[z, 0, 2] Subscript[z, 2, 0] + 
     Subscript[z^2, 1, 1]) + 
  2 λ (Subscript[z, 0, 
      1] ((-Subscript[z, 0, 2] + Subscript[z, 2, 
           0]) Subscript[λ, 0, 1] - 
        2 Subscript[z, 1, 1] Subscript[λ, 1, 0]) + 
     Subscript[z^2, 0, 
      1] (Subscript[λ, 0, 2] + Subscript[λ, 2, 
        0]) + Subscript[z, 1, 
      0] (-2 Subscript[z, 1, 1] Subscript[λ, 0, 
         1] + (Subscript[z, 0, 2] - Subscript[z, 2, 
           0]) Subscript[λ, 1, 0] + 
        Subscript[z, 1, 
         0] (Subscript[λ, 0, 2] + Subscript[λ, 2, 
           0]))) - (Subscript[z^2, 0, 1] + Subscript[z^2, 1, 
     0]) (Subscript[λ^2, 0, 1] + Subscript[λ^2, 1,
      0]) + 2 λ^3 ((Subscript[z, 0, 2] + Subscript[z, 2, 
        0]) Derivative[1][f][
       z] + (Subscript[z^2, 0, 1] + Subscript[z^2, 1, 0]) (
       f^\[Prime]\[Prime])[z])) + 2 λ f[
 z] ((Subscript[z^2, 0, 1] + Subscript[z^2, 1, 
     0]) (Subscript[z, 0, 1] Subscript[λ, 0, 1] + 
     Subscript[z, 1, 0] Subscript[λ, 1, 0]) Derivative[1][
    f][z] - λ^2 (Subscript[z^2, 0, 1] + Subscript[z^2, 1, 
     0]) Derivative[1][f][
    z]^2 + λ (2 (-2 Subscript[z, 0, 1] Subscript[z, 1, 0]
          Subscript[z, 1, 1] + 
        Subscript[z, 2, 0] Subscript[z^2, 0, 1] + 
        Subscript[z, 0, 2] Subscript[z^2, 1, 0]) Derivative[1][f][
       z] + (Subscript[z^2, 0, 1] + Subscript[z^2, 1, 0])^2 (
       f^\[Prime]\[Prime])[z])))/(4 λ f[
z] (λ f[z] + Subscript[z^2, 0, 1] + Subscript[z^2, 1, 0]))

and I want to collect the terms of the type

Subscript[z, 0, 1]

and

Subscript[z^2, 0, 1]

here 0, and 1 can be change.

I can do for the first one as

Collect[ expr// ExpandAll, Subscript[z, _, _], Simplify]

but while I try to use

Collect[ expr// ExpandAll, Subscript[z^2, _, _], Simplify]

to collect the second one, it doesn't work, Why?

What's more, can I write a pattern that will collect both of them at the same time?

Answer 1

As Chris mentioned in the comments above, the following seems to work:

Collect[expr // Together // Numerator, Subscript[z^2, _, _], Simplify]