code: def test_expand_negative_integer_powers():
      expr = (x + y) ** (-2)
      assert expr.expand() == 1 / (2 * x * y + x**2 + y**2)
      assert expr.expand(multinomial=False) == (x + y) ** (-2)
      expr = (x + y) ** (-3)
      assert expr.expand() == 1 / (
          3 * x * x * y + 3 * x * y * y + x**3 + y**3
      )
      assert expr.expand(multinomial=False) == (x + y) ** (-3)
      expr = (x + y) ** (2) * (x + y) ** (-4)
      assert expr.expand() == 1 / (2 * x * y + x**2 + y**2)
      assert expr.expand(multinomial=False) == (x + y) ** (-2)
  
imports: from sympy.core.expr import unchanged
  from sympy.core.mul import Mul
  from sympy.core.numbers import I, Rational, pi
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.series.order import O
  from sympy.simplify.radsimp import expand_numer
  from sympy.core.function import expand, expand_multinomial, expand_power_base, expand_log
  from sympy.testing.pytest import raises
  from sympy.core.random import verify_numerically
  from sympy.abc import x, y, z
label_desc: Use image node_id 3 for calling a global function with example usage: test_expand_negative_integer_powers() without return types