diff --git a/dimod/higherorder/utils.py b/dimod/higherorder/utils.py
index 242a0ad78..33535a49d 100644
--- a/dimod/higherorder/utils.py
+++ b/dimod/higherorder/utils.py
@@ -297,10 +297,27 @@ def make_quadratic(poly: Union[Polynomial, BinaryPolynomial], strength: float,
             Terms of the reduced polynomial are added to this binary quadratic model.
             If not provided, a new binary quadratic model is created.
 
+    Returns:
+        :class:`~dimod.binary.BinaryQuadraticModel`: A binary quadratic model
+        with three types of variables:
+
+        *   Original variables: Variables mapped directly from the input
+            polynomial (e.g., ``0``, ``1``, ``12``).
+        *   Product variables: Intermediate variables introduced to reduce
+            higher-order terms, representing the product of two variables. These
+            are typically named by joining the original variables (e.g., ``0*1``
+            represents the product of ``0`` and ``1``).
+        *   Auxiliary variables: Variables introduced to enforce the penalty
+            constraints that ensure the mathematical relationship of the product
+            variables holds true at the ground state (e.g., ``aux0,1`` enforces
+            the constraint for ``0*1``).
+
     Examples:
 
         >>> poly = {(0,): -1, (1,): 1, (2,): 1.5, (0, 1): -1, (0, 1, 2): -2}
         >>> bqm = dimod.make_quadratic(poly, 5.0, dimod.SPIN)
+        >>> bqm
+        BinaryQuadraticModel({0: -3.5, 1: -1.5, '0*1': -2.5, 'aux0,1': -5.0, 2: 1.5}, {(1, 0): 1.5, ('0*1', 0): 2.5, ('0*1', 1): 2.5, ('aux0,1', 0): 5.0, ('aux0,1', 1): 5.0, ('aux0,1', '0*1'): 5.0, (2, '0*1'): -2.0}, 10.0, 'SPIN')
 
     """
     from dimod.generators import and_gate