Factorize (n * x) + (n * y) to become n * (x + y) and multiply_out to do reverse.

factorize.ml

type expr =
  | Plus of expr * expr
  | Minus of expr * expr
  | Times of expr * expr
  | Divide of expr * expr
  | Value of string

let rec to_string e =
  match e with
  | Plus (left, right) ->
    "(" ^ to_string left ^ " + " ^ to_string right ^ ")"
  | Minus (left, right) ->
    "(" ^ to_string left ^ " - " ^ to_string right ^ ")"
  | Times (left, right) ->
    "(" ^ to_string left ^ " * " ^ to_string right ^ ")"
  | Divide (left, right) ->
    "(" ^ to_string left ^ " / " ^ to_string right ^ ")"
  | Value v -> v;;

let rec multiply_out e =
  match e with
  | Times (e1, Plus (e2, e3)) ->
    Plus (Times (multiply_out e1, multiply_out e2),
          Times (multiply_out e1, multiply_out e3))
  | Times (Plus (e1, e2), e3) ->
    Plus (Times (multiply_out e1, multiply_out e3),
          Times (multiply_out e2, multiply_out e3))
  | Plus (left, right) ->
    Plus (multiply_out left, multiply_out right)
  | Minus (left, right) ->
    Minus (multiply_out left, multiply_out right)
  | Times (left, right) ->
    Times (multiply_out left, multiply_out right)
  | Divide (left, right) ->
    Divide (multiply_out left, multiply_out right)
  | Value v -> Value v;;

let factorize e =
  match e with
  | Plus (Times (e1, e2), Times (e3, e4)) when e1 = e3 ->
    Times (e1, Plus (e2, e4))
  | Plus (Times (e1, e2), Times (e3, e4)) when e2 = e4 ->
    Times (Plus (e1, e3), e4)
  | e -> e;;

let print_expr e =
  print_endline (to_string e);;

print_expr (Times (Value "n", Plus (Value "x", Value "y")));;
print_expr (multiply_out (Times (Value "n", Plus (Value "x", Value "y"))));;
print_expr (factorize (Plus (Times (Value "n", Value "x"), Times (Value "n", Value "y"))));;