diff --git a/src/Bridges/Variable/kernel.jl b/src/Bridges/Variable/kernel.jl
index cf438f7a4..231a83bfb 100644
--- a/src/Bridges/Variable/kernel.jl
+++ b/src/Bridges/Variable/kernel.jl
@@ -20,7 +20,11 @@ function MOI.Bridges.Variable.bridge_constrained_variable(
         gram, vars, con = SOS.add_gram_matrix(model, M, gram_basis, T)
         push!(variables, vars)
         push!(constraints, con)
-        MA.operate!(SA.UnsafeAddMul(*), acc, gram, weight)
+        if isone(weight)
+            MA.operate!(SA.UnsafeAdd(), acc, SA.QuadraticForm(gram))
+        else
+            MA.operate!(SA.UnsafeAddMul(*), acc, gram, weight)
+        end
     end
     MA.operate!(SA.canonical, SA.coeffs(acc))
     return KernelBridge{T,M}(
diff --git a/src/Certificate/ideal.jl b/src/Certificate/ideal.jl
index 20bc096d3..920358ac4 100644
--- a/src/Certificate/ideal.jl
+++ b/src/Certificate/ideal.jl
@@ -29,12 +29,20 @@ function _combine_with_gram(
         )
     end
     for (gram, weight) in zip(gram_bases, weights)
-        MA.operate!(
-            SA.UnsafeAddMul(*),
-            p,
-            GramMatrix{_NonZero}((_, _) -> _NonZero(), gram),
-            weight,
-        )
+        if isone(weight)
+            MA.operate!(
+                SA.UnsafeAdd(),
+                p,
+                SA.QuadraticForm(GramMatrix{_NonZero}((_, _) -> _NonZero(), gram)),
+            )
+        else
+            MA.operate!(
+                SA.UnsafeAddMul(*),
+                p,
+                GramMatrix{_NonZero}((_, _) -> _NonZero(), gram),
+                weight,
+            )
+        end
     end
     MA.operate!(SA.canonical, SA.coeffs(p))
     return MB.SubBasis{B}(keys(SA.coeffs(p)))