calc 16 * x ^ 2 * y ^ 2 * (x + y) ^ 2 ≤ ((x + y) ^ 2) ^ 2 * (x + y) ^ 2 := by gcongr; linarith
  _ = ((x + y) ^ 2) ^ 3 := by ring
x y : ℝ
hxy : 0 ≤ x * y
this : (x - y) ^ 2 * ((x + y) ^ 2 + 4 * (x * y)) ≥ 0
⊢ 16 * x ^ 2 * y ^ 2 * (x + y) ^ 2 ≤ ((x + y) ^ 2) ^ 3
no goals