diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 997cef7b09576..f29930b010795 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1112,6 +1112,41 @@ def _cmp_method(self, other, op):
     __divmod__ = make_invalid_op("__divmod__")
     __rdivmod__ = make_invalid_op("__rdivmod__")
 
+    @final
+    def _get_i8_values_and_mask(
+        self, other
+    ) -> tuple[int | npt.NDArray[np.int64], None | npt.NDArray[np.bool_]]:
+        """
+        Get the int64 values and b_mask to pass to checked_add_with_arr.
+        """
+        if isinstance(other, Period):
+            i8values = other.ordinal
+            mask = None
+        elif isinstance(other, Timestamp):
+            i8values = other.value
+            mask = None
+        else:
+            # PeriodArray, DatetimeArray, TimedeltaArray
+            mask = other._isnan
+            i8values = other.asi8
+        return i8values, mask
+
+    @final
+    def _get_arithmetic_result_freq(self, other) -> BaseOffset | None:
+        """
+        Check if we can preserve self.freq in addition or subtraction.
+        """
+        # Adding or subtracting a Timedelta/Timestamp scalar is freq-preserving
+        #  whenever self.freq is a Tick
+        if is_period_dtype(self.dtype):
+            return self.freq
+        elif not lib.is_scalar(other):
+            return None
+        elif isinstance(self.freq, Tick):
+            # In these cases
+            return self.freq
+        return None
+
     @final
     def _add_datetimelike_scalar(self, other) -> DatetimeArray:
         if not is_timedelta64_dtype(self.dtype):
@@ -1228,15 +1263,7 @@ def _sub_period(self, other: Period) -> npt.NDArray[np.object_]:
         # If the operation is well-defined, we return an object-dtype ndarray
         # of DateOffsets.  Null entries are filled with pd.NaT
         self._check_compatible_with(other)
-        new_i8_data = checked_add_with_arr(
-            self.asi8, -other.ordinal, arr_mask=self._isnan
-        )
-        new_data = np.array([self.freq.base * x for x in new_i8_data])
-
-        if self._hasna:
-            new_data[self._isnan] = NaT
-
-        return new_data
+        return self._sub_periodlike(other)
 
     @final
     def _add_period(self, other: Period) -> PeriodArray:
@@ -1361,15 +1388,26 @@ def _sub_period_array(self, other: PeriodArray) -> npt.NDArray[np.object_]:
         self = cast("PeriodArray", self)
         self._require_matching_freq(other)
 
-        new_i8_values = checked_add_with_arr(
-            self.asi8, -other.asi8, arr_mask=self._isnan, b_mask=other._isnan
+        return self._sub_periodlike(other)
+
+    @final
+    def _sub_periodlike(self, other: Period | PeriodArray) -> npt.NDArray[np.object_]:
+        # caller is responsible for calling
+        #  require_matching_freq/check_compatible_with
+        other_i8, o_mask = self._get_i8_values_and_mask(other)
+        new_i8_data = checked_add_with_arr(
+            self.asi8, -other_i8, arr_mask=self._isnan, b_mask=o_mask
         )
+        new_data = np.array([self.freq.base * x for x in new_i8_data])
 
-        new_values = np.array([self.freq.base * x for x in new_i8_values])
-        if self._hasna or other._hasna:
-            mask = self._isnan | other._isnan
-            new_values[mask] = NaT
-        return new_values
+        if o_mask is None:
+            # i.e. Period scalar
+            mask = self._isnan
+        else:
+            # i.e. PeriodArray
+            mask = self._isnan | o_mask
+        new_data[mask] = NaT
+        return new_data
 
     @final
     def _addsub_object_array(self, other: np.ndarray, op):