diff --git a/src/rewrite.jl b/src/rewrite.jl
index 44d43a7..811570f 100644
--- a/src/rewrite.jl
+++ b/src/rewrite.jl
@@ -79,6 +79,21 @@ function Base.:/(z::Zero, x::Any)
     end
 end
 
+# These methods are used to provide an efficient implementation for the common
+# case like `x^2 * sum(f for i in 1:0)`, which lowers to
+# `_MA.operate!!(*, x^2, _MA.Zero())`. We don't need the method with reversed
+# arguments because MA.Zero is not mutable, and MA never queries the mutablility
+# of arguments if the first is not mutable.
+promote_operation(::typeof(*), ::Type{<:Any}, ::Type{Zero}) = Zero
+
+function promote_operation(
+    ::typeof(*),
+    ::Type{<:AbstractArray{T}},
+    ::Type{Zero},
+) where {T}
+    return Zero
+end
+
 # Needed by `@rewrite(BigInt(1) .+ sum(1 for i in 1:0) * 1^2)`
 # since we don't require mutable type to support Zero in
 # `mutable_operate!`.
diff --git a/test/rewrite.jl b/test/rewrite.jl
index e2d1c8a..840174b 100644
--- a/test/rewrite.jl
+++ b/test/rewrite.jl
@@ -199,3 +199,70 @@ end
     b = @allocated MA.operate(LinearAlgebra.dot, x, y)
     @test a == b
 end
+
+@testset "test_multiply_expr_MA_Zero" begin
+    x = DummyBigInt(1)
+    f = DummyBigInt(2)
+    @test MA.@rewrite(
+        f * sum(x for i in 1:0),
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        sum(x for i in 1:0) * f,
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        -f * sum(x for i in 1:0),
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        sum(x for i in 1:0) * -f,
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        (f + f) * sum(x for i in 1:0),
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        sum(x for i in 1:0) * (f + f),
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        -[f] * sum(x for i in 1:0),
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.@rewrite(
+        sum(x for i in 1:0) * -[f],
+        move_factors_into_sums = false
+    ) == MA.Zero()
+    @test MA.isequal_canonical(
+        MA.@rewrite(f + sum(x for i in 1:0), move_factors_into_sums = false),
+        f,
+    )
+    @test MA.isequal_canonical(
+        MA.@rewrite(sum(x for i in 1:0) + f, move_factors_into_sums = false),
+        f,
+    )
+    @test MA.isequal_canonical(
+        MA.@rewrite(-f + sum(x for i in 1:0), move_factors_into_sums = false),
+        -f,
+    )
+    @test MA.isequal_canonical(
+        MA.@rewrite(sum(x for i in 1:0) + -f, move_factors_into_sums = false),
+        -f,
+    )
+    @test MA.isequal_canonical(
+        MA.@rewrite(
+            (f + f) + sum(x for i in 1:0),
+            move_factors_into_sums = false
+        ),
+        f + f,
+    )
+    @test MA.isequal_canonical(
+        MA.@rewrite(
+            sum(x for i in 1:0) + (f + f),
+            move_factors_into_sums = false
+        ),
+        f + f,
+    )
+end