diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 6cb597ba75852..7447d593a7ff0 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -1206,7 +1206,7 @@ def _maybe_convert(arr):
 
             return _maybe_convert(res)
 
-        op_name = ops._get_op_name(op, True)
+        op_name = f"__{op.__name__}__"
         return set_function_name(_binop, op_name, cls)
 
     @classmethod
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index df58593bc930c..d9a93ac7ba289 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3286,7 +3286,7 @@ def reindex(self, target, method=None, level=None, limit=None, tolerance=None):
         preserve_names = not hasattr(target, "name")
 
         # GH7774: preserve dtype/tz if target is empty and not an Index.
-        target = _ensure_has_len(target)  # target may be an iterator
+        target = ensure_has_len(target)  # target may be an iterator
 
         if not isinstance(target, Index) and len(target) == 0:
             if isinstance(self, ABCRangeIndex):
@@ -5573,7 +5573,7 @@ def ensure_index(index_like, copy: bool = False):
     return Index(index_like)
 
 
-def _ensure_has_len(seq):
+def ensure_has_len(seq):
     """
     If seq is an iterator, put its values into a list.
     """
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 7aa1456846612..9126a7a3309d2 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2288,7 +2288,7 @@ def reindex(self, target, method=None, level=None, limit=None, tolerance=None):
 
             # GH7774: preserve dtype/tz if target is empty and not an Index.
             # target may be an iterator
-            target = ibase._ensure_has_len(target)
+            target = ibase.ensure_has_len(target)
             if len(target) == 0 and not isinstance(target, Index):
                 idx = self.levels[level]
                 attrs = idx._get_attributes_dict()
diff --git a/pandas/core/ops/__init__.py b/pandas/core/ops/__init__.py
index d6ba9d763366b..c14c4a311d66c 100644
--- a/pandas/core/ops/__init__.py
+++ b/pandas/core/ops/__init__.py
@@ -10,7 +10,7 @@
 
 from pandas._libs import lib
 from pandas._libs.ops_dispatch import maybe_dispatch_ufunc_to_dunder_op  # noqa:F401
-from pandas._typing import ArrayLike, Level
+from pandas._typing import Level
 from pandas.util._decorators import Appender
 
 from pandas.core.dtypes.common import is_list_like
@@ -224,7 +224,7 @@ def _get_opstr(op):
     }[op]
 
 
-def _get_op_name(op, special):
+def _get_op_name(op, special: bool) -> str:
     """
     Find the name to attach to this method according to conventions
     for special and non-special methods.
@@ -385,42 +385,6 @@ def _align_method_SERIES(left, right, align_asobject=False):
     return left, right
 
 
-def _construct_result(
-    left: ABCSeries, result: ArrayLike, index: ABCIndexClass, name,
-):
-    """
-    Construct an appropriately-labelled Series from the result of an op.
-
-    Parameters
-    ----------
-    left : Series
-    result : ndarray or ExtensionArray
-    index : Index
-    name : object
-
-    Returns
-    -------
-    Series
-        In the case of __divmod__ or __rdivmod__, a 2-tuple of Series.
-    """
-    if isinstance(result, tuple):
-        # produced by divmod or rdivmod
-        return (
-            _construct_result(left, result[0], index=index, name=name),
-            _construct_result(left, result[1], index=index, name=name),
-        )
-
-    # We do not pass dtype to ensure that the Series constructor
-    #  does inference in the case where `result` has object-dtype.
-    out = left._constructor(result, index=index)
-    out = out.__finalize__(left)
-
-    # Set the result's name after __finalize__ is called because __finalize__
-    #  would set it back to self.name
-    out.name = name
-    return out
-
-
 def _arith_method_SERIES(cls, op, special):
     """
     Wrapper function for Series arithmetic operations, to avoid
@@ -439,7 +403,7 @@ def wrapper(left, right):
         rvalues = extract_array(right, extract_numpy=True)
         result = arithmetic_op(lvalues, rvalues, op, str_rep)
 
-        return _construct_result(left, result, index=left.index, name=res_name)
+        return left._construct_result(result, name=res_name)
 
     wrapper.__name__ = op_name
     return wrapper
@@ -466,7 +430,7 @@ def wrapper(self, other):
 
         res_values = comparison_op(lvalues, rvalues, op, str_rep)
 
-        return _construct_result(self, res_values, index=self.index, name=res_name)
+        return self._construct_result(res_values, name=res_name)
 
     wrapper.__name__ = op_name
     return wrapper
@@ -488,7 +452,7 @@ def wrapper(self, other):
         rvalues = extract_array(other, extract_numpy=True)
 
         res_values = logical_op(lvalues, rvalues, op)
-        return _construct_result(self, res_values, index=self.index, name=res_name)
+        return self._construct_result(res_values, name=res_name)
 
     wrapper.__name__ = op_name
     return wrapper
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 2f4ca61a402dc..78368ee9f6851 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -14,6 +14,7 @@
     Optional,
     Tuple,
     Type,
+    Union,
 )
 import warnings
 
@@ -22,7 +23,7 @@
 from pandas._config import get_option
 
 from pandas._libs import lib, properties, reshape, tslibs
-from pandas._typing import Axis, DtypeObj, Label
+from pandas._typing import ArrayLike, Axis, DtypeObj, Label
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution, doc
 from pandas.util._validators import validate_bool_kwarg, validate_percentile
@@ -2623,12 +2624,10 @@ def _binop(self, other, func, level=None, fill_value=None):
         if not isinstance(other, Series):
             raise AssertionError("Other operand must be Series")
 
-        new_index = self.index
         this = self
 
         if not self.index.equals(other.index):
             this, other = self.align(other, level=level, join="outer", copy=False)
-            new_index = this.index
 
         this_vals, other_vals = ops.fill_binop(this.values, other.values, fill_value)
 
@@ -2636,9 +2635,46 @@ def _binop(self, other, func, level=None, fill_value=None):
             result = func(this_vals, other_vals)
 
         name = ops.get_op_result_name(self, other)
-        ret = ops._construct_result(self, result, new_index, name)
+        ret = this._construct_result(result, name)
         return ret
 
+    def _construct_result(
+        self, result: Union[ArrayLike, Tuple[ArrayLike, ArrayLike]], name: Label
+    ) -> Union["Series", Tuple["Series", "Series"]]:
+        """
+        Construct an appropriately-labelled Series from the result of an op.
+
+        Parameters
+        ----------
+        result : ndarray or ExtensionArray
+        name : Label
+
+        Returns
+        -------
+        Series
+            In the case of __divmod__ or __rdivmod__, a 2-tuple of Series.
+        """
+        if isinstance(result, tuple):
+            # produced by divmod or rdivmod
+
+            res1 = self._construct_result(result[0], name=name)
+            res2 = self._construct_result(result[1], name=name)
+
+            # GH#33427 assertions to keep mypy happy
+            assert isinstance(res1, Series)
+            assert isinstance(res2, Series)
+            return (res1, res2)
+
+        # We do not pass dtype to ensure that the Series constructor
+        #  does inference in the case where `result` has object-dtype.
+        out = self._constructor(result, index=self.index)
+        out = out.__finalize__(self)
+
+        # Set the result's name after __finalize__ is called because __finalize__
+        #  would set it back to self.name
+        out.name = name
+        return out
+
     def combine(self, other, func, fill_value=None) -> "Series":
         """
         Combine the Series with a Series or scalar according to `func`.