diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 33165ce2..fa6df6a9 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -125,6 +125,22 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         ExtensionAlgebraTarget(res.try_into().unwrap())
     }
 
+    /// Add 3 `ExtensionTarget`s with 1 `ArithmeticExtensionGate`s.
+    pub fn add_three_extension(
+        &mut self,
+        a: ExtensionTarget<D>,
+        b: ExtensionTarget<D>,
+        c: ExtensionTarget<D>,
+    ) -> ExtensionTarget<D> {
+        let one = self.one_extension();
+        let gate = self.num_gates();
+        let first_out =
+            ExtensionTarget::from_range(gate, ArithmeticExtensionGate::<D>::wires_first_output());
+        self.double_arithmetic_extension(F::ONE, F::ONE, one, a, b, one, c, first_out)
+            .1
+    }
+
+    /// Add `n` `ExtensionTarget`s with `n/2 + 1` `ArithmeticExtensionGate`s.
     pub fn add_many_extension(&mut self, terms: &[ExtensionTarget<D>]) -> ExtensionTarget<D> {
         let zero = self.zero_extension();
         let mut terms = terms.to_vec();
@@ -246,6 +262,22 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         ExtensionAlgebraTarget(res)
     }
 
+    /// Multiply 3 `ExtensionTarget`s with 1 `ArithmeticExtensionGate`s.
+    pub fn mul_three_extension(
+        &mut self,
+        a: ExtensionTarget<D>,
+        b: ExtensionTarget<D>,
+        c: ExtensionTarget<D>,
+    ) -> ExtensionTarget<D> {
+        let zero = self.zero_extension();
+        let gate = self.num_gates();
+        let first_out =
+            ExtensionTarget::from_range(gate, ArithmeticExtensionGate::<D>::wires_first_output());
+        self.double_arithmetic_extension(F::ONE, F::ZERO, a, b, zero, c, first_out, zero)
+            .1
+    }
+
+    /// Multiply `n` `ExtensionTarget`s with `n/2 + 1` `ArithmeticExtensionGate`s.
     pub fn mul_many_extension(&mut self, terms: &[ExtensionTarget<D>]) -> ExtensionTarget<D> {
         let one = self.one_extension();
         let mut terms = terms.to_vec();
@@ -487,8 +519,8 @@ mod tests {
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let mut pw = PartialWitness::new();
 
-        let vs = FF::rand_vec(20);
-        let ts = builder.add_virtual_extension_targets(20);
+        let vs = FF::rand_vec(3);
+        let ts = builder.add_virtual_extension_targets(3);
         for (&v, &t) in vs.iter().zip(&ts) {
             pw.set_extension_target(t, v);
         }
@@ -500,10 +532,12 @@ mod tests {
             }
             acc
         };
-        let mul2 = builder.constant_extension(vs.into_iter().product());
+        let mul2 = builder.mul_three_extension(ts[0], ts[1], ts[2]);
+        let mul3 = builder.constant_extension(vs.into_iter().product());
 
         builder.assert_equal_extension(mul0, mul1);
         builder.assert_equal_extension(mul1, mul2);
+        builder.assert_equal_extension(mul2, mul3);
 
         let data = builder.build();
         let proof = data.prove(pw)?;