diff --git a/poincare/Makefile b/poincare/Makefile
index 1408138a6..a3d430325 100644
--- a/poincare/Makefile
+++ b/poincare/Makefile
@@ -25,7 +25,7 @@ objs += $(addprefix poincare/src/layout/,\
 )
 objs += $(addprefix poincare/src/simplify/,\
   simplify_addition_integer.o\
-  simplify_addition_merge.o\
+  simplify_commutative_merge.o\
   simplify_product_zero.o\
 )
 tests += $(addprefix poincare/test/,\
diff --git a/poincare/src/expression.cpp b/poincare/src/expression.cpp
index 77bc0bc8a..934d680a1 100644
--- a/poincare/src/expression.cpp
+++ b/poincare/src/expression.cpp
@@ -4,7 +4,7 @@
 #include "simplify/simplify.h"
 #include "simplify/simplify_product_zero.h"
 #include "simplify/simplify_addition_integer.h"
-#include "simplify/simplify_addition_merge.h"
+#include "simplify/simplify_commutative_merge.h"
 extern "C" {
 #include <assert.h>
 }
@@ -13,7 +13,7 @@ extern "C" {
 static expression_simplifier_t kSimplifiers[] = {
   &SimplifyProductZero,
   &SimplifyAdditionInteger,
-  &SimplifyAdditionMerge,
+  &SimplifyCommutativeMerge,
   nullptr
 };
 
diff --git a/poincare/src/simplify/simplify_addition_merge.cpp b/poincare/src/simplify/simplify_addition_merge.cpp
deleted file mode 100644
index 9add4fc37..000000000
--- a/poincare/src/simplify/simplify_addition_merge.cpp
+++ /dev/null
@@ -1,43 +0,0 @@
-#include "simplify_addition_merge.h"
-#include <poincare/addition.h>
-extern "C" {
-#include <stdlib.h>
-#include <assert.h>
-}
-
-Expression * SimplifyAdditionMerge(Expression * e) {
-  if (e->type() != Expression::Type::Addition) {
-    return nullptr;
-  }
-  Addition * a = (Addition *)e;
-  // Let's count how many elements we'll be able to pick up from our children
-  int mergedNumberOfChildren = 0;
-  for (int i=0; i<a->numberOfOperands(); i++) {
-    Expression * operand = a->operand(i);
-    if (operand->type() == Expression::Type::Addition) {
-      mergedNumberOfChildren += operand->numberOfOperands();
-    } else {
-      mergedNumberOfChildren += 1;
-    }
-  }
-  assert(mergedNumberOfChildren >= a->numberOfOperands());
-  if (mergedNumberOfChildren == a->numberOfOperands()) {
-    // Nothing to simplify here
-    return nullptr;
-  }
-  Expression ** children = (Expression **)malloc(sizeof(Expression *) * mergedNumberOfChildren);
-  int childrenIndex = 0;
-  for (int i=0; i<a->numberOfOperands(); i++) {
-    Expression * operand = a->operand(i);
-    if (operand->type() == Expression::Type::Addition) {
-      for (int j=0; j<operand->numberOfOperands(); j++) {
-        children[childrenIndex++] = operand->operand(j);
-      }
-    } else {
-      children[childrenIndex++] = operand;
-    }
-  }
-  Addition * result = new Addition(children, mergedNumberOfChildren, true);
-  free(children);
-  return result;
-}
diff --git a/poincare/src/simplify/simplify_addition_merge.h b/poincare/src/simplify/simplify_addition_merge.h
deleted file mode 100644
index fb80bcfa6..000000000
--- a/poincare/src/simplify/simplify_addition_merge.h
+++ /dev/null
@@ -1,16 +0,0 @@
-#ifndef POINCARE_SIMPLIFY_ADDITION_MERGE_H
-#define POINCARE_SIMPLIFY_ADDITION_MERGE_H
-
-#include "simplify.h"
-
-/*
- *   +                  +
- *  / \               / | \
- * a   +         ->  a  c  d
- *    / \
- *   c   d
- */
-
-Expression * SimplifyAdditionMerge(Expression * e);
-
-#endif
diff --git a/poincare/src/simplify/simplify_commutative_merge.cpp b/poincare/src/simplify/simplify_commutative_merge.cpp
new file mode 100644
index 000000000..328c577b5
--- /dev/null
+++ b/poincare/src/simplify/simplify_commutative_merge.cpp
@@ -0,0 +1,55 @@
+#include "simplify_commutative_merge.h"
+#include <poincare/addition.h>
+#include <poincare/product.h>
+extern "C" {
+#include <stdlib.h>
+#include <assert.h>
+}
+
+Expression * SimplifyCommutativeMerge(Expression * e) {
+  if (e->type() != Expression::Type::Addition &&
+      e->type() != Expression::Type::Product) {
+    return nullptr;
+  }
+  CommutativeOperation * c = (CommutativeOperation *)e;
+  // Let's count how many elements we'll be able to pick up from our children
+  int mergedNumberOfChildren = 0;
+  for (int i=0; i<c->numberOfOperands(); i++) {
+    Expression * operand = c->operand(i);
+    if (operand->type() == c->type()) {
+      mergedNumberOfChildren += operand->numberOfOperands();
+    } else {
+      mergedNumberOfChildren += 1;
+    }
+  }
+  assert(mergedNumberOfChildren >= c->numberOfOperands());
+  if (mergedNumberOfChildren == c->numberOfOperands()) {
+    // Nothing to simplify here
+    return nullptr;
+  }
+  Expression ** children = (Expression **)malloc(sizeof(Expression *) * mergedNumberOfChildren);
+  int childrenIndex = 0;
+  for (int i=0; i<c->numberOfOperands(); i++) {
+    Expression * operand = c->operand(i);
+    if (operand->type() == c->type()) {
+      for (int j=0; j<operand->numberOfOperands(); j++) {
+        children[childrenIndex++] = operand->operand(j);
+      }
+    } else {
+      children[childrenIndex++] = operand;
+    }
+  }
+  CommutativeOperation * result = nullptr;
+  switch(e->type()) {
+    case Expression::Type::Addition:
+      result = new Addition(children, mergedNumberOfChildren, true);
+      break;
+    case Expression::Type::Product:
+      result = new Product(children, mergedNumberOfChildren, true);
+      break;
+    default:
+      assert(false);
+  }
+  free(children);
+  return result;
+}
diff --git a/poincare/src/simplify/simplify_commutative_merge.h b/poincare/src/simplify/simplify_commutative_merge.h
new file mode 100644
index 000000000..057049a37
--- /dev/null
+++ b/poincare/src/simplify/simplify_commutative_merge.h
@@ -0,0 +1,16 @@
+#ifndef POINCARE_SIMPLIFY_COMMUTATIVE_MERGE_H
+#define POINCARE_SIMPLIFY_COMMUTATIVE_MERGE_H
+
+#include "simplify.h"
+
+/*
+ *   +                  +
+ *  / \               / | \
+ * a   +         ->  a  c  d
+ *    / \
+ *   c   d
+ */
+
+Expression * SimplifyCommutativeMerge(Expression * e);
+
+#endif