diff --git a/datafusion/optimizer/src/simplify_expressions.rs b/datafusion/optimizer/src/simplify_expressions.rs
index 4aee2fd0378a..94a035fbd64e 100644
--- a/datafusion/optimizer/src/simplify_expressions.rs
+++ b/datafusion/optimizer/src/simplify_expressions.rs
@@ -72,7 +72,7 @@ impl<'a, 'b> SimplifyInfo for SimplifyContext<'a, 'b> {
                 // This means we weren't able to compute `Expr::nullable` with
                 // *any* input schemas, signalling a problem
                 DataFusionError::Internal(format!(
-                    "Could not find find columns in '{}' during simplify",
+                    "Could not find columns in '{}' during simplify",
                     expr
                 ))
             })
@@ -110,6 +110,22 @@ fn expr_contains(expr: &Expr, needle: &Expr, search_op: Operator) -> bool {
     }
 }
 
+fn is_zero(s: &Expr) -> bool {
+    match s {
+        Expr::Literal(ScalarValue::Int8(Some(0)))
+        | Expr::Literal(ScalarValue::Int16(Some(0)))
+        | Expr::Literal(ScalarValue::Int32(Some(0)))
+        | Expr::Literal(ScalarValue::Int64(Some(0)))
+        | Expr::Literal(ScalarValue::UInt8(Some(0)))
+        | Expr::Literal(ScalarValue::UInt16(Some(0)))
+        | Expr::Literal(ScalarValue::UInt32(Some(0)))
+        | Expr::Literal(ScalarValue::UInt64(Some(0))) => true,
+        Expr::Literal(ScalarValue::Float32(Some(v))) if *v == 0. => true,
+        Expr::Literal(ScalarValue::Float64(Some(v))) if *v == 0. => true,
+        _ => false,
+    }
+}
+
 fn is_one(s: &Expr) -> bool {
     match s {
         Expr::Literal(ScalarValue::Int8(Some(1)))
@@ -728,16 +744,44 @@ impl<'a, S: SimplifyInfo> ExprRewriter for Simplifier<'a, S> {
             //
             // Rules for Multiply
             //
+
+            // A * 1 --> A
             BinaryExpr {
                 left,
                 op: Multiply,
                 right,
             } if is_one(&right) => *left,
+            // 1 * A --> A
             BinaryExpr {
                 left,
                 op: Multiply,
                 right,
             } if is_one(&left) => *right,
+            // A * null --> null
+            BinaryExpr {
+                left: _,
+                op: Multiply,
+                right,
+            } if is_null(&right) => *right,
+            // null * A --> null
+            BinaryExpr {
+                left,
+                op: Multiply,
+                right: _,
+            } if is_null(&left) => *left,
+
+            // A * 0 --> 0 (if A is not null)
+            BinaryExpr {
+                left,
+                op: Multiply,
+                right,
+            } if !info.nullable(&left)? && is_zero(&right) => *right,
+            // 0 * A --> 0 (if A is not null)
+            BinaryExpr {
+                left,
+                op: Multiply,
+                right,
+            } if !info.nullable(&right)? && is_zero(&left) => *left,
 
             //
             // Rules for Divide
@@ -971,6 +1015,43 @@ mod tests {
         assert_eq!(simplify(expr_b), expected);
     }
 
+    #[test]
+    fn test_simplify_multiply_by_null() {
+        let null = Expr::Literal(ScalarValue::Null);
+        // A * null --> null
+        {
+            let expr = binary_expr(col("c2"), Operator::Multiply, null.clone());
+            assert_eq!(simplify(expr), null);
+        }
+        // null * A --> null
+        {
+            let expr = binary_expr(null.clone(), Operator::Multiply, col("c2"));
+            assert_eq!(simplify(expr), null);
+        }
+    }
+
+    #[test]
+    fn test_simplify_multiply_by_zero() {
+        // cannot optimize A * null (null * A) if A is nullable
+        {
+            let expr_a = binary_expr(col("c2"), Operator::Multiply, lit(0));
+            let expr_b = binary_expr(lit(0), Operator::Multiply, col("c2"));
+
+            assert_eq!(simplify(expr_a.clone()), expr_a);
+            assert_eq!(simplify(expr_b.clone()), expr_b);
+        }
+        // 0 * A --> 0 if A is not nullable
+        {
+            let expr = binary_expr(lit(0), Operator::Multiply, col("c2_non_null"));
+            assert_eq!(simplify(expr), lit(0));
+        }
+        // A * 0 --> 0 if A is not nullable
+        {
+            let expr = binary_expr(col("c2_non_null"), Operator::Multiply, lit(0));
+            assert_eq!(simplify(expr), lit(0));
+        }
+    }
+
     #[test]
     fn test_simplify_divide_by_one() {
         let expr = binary_expr(col("c2"), Operator::Divide, lit(1));