rewrite error: "failed"

Stream: general

[Kenny Lau]

example (x y z : ℕ) : x * (y + z) = x * y + x * z :=
by rw add_mul

/-
failed
state:
x y z : ℕ
⊢ x * (y + z) = x * y + x * z
-/

example (x y z : ℕ) : x * (y + z) = x * y + x * z :=
by rw nat.pow_two

/-
rewrite tactic failed, did not find instance of the pattern in the target expression
  ?m_1 ^ 2
state:
x y z : ℕ
⊢ x * (y + z) = x * y + x * z
-/

[Kenny Lau]

could we modify rw to make the error more precise in the first case?