1. Stating the problem: Simplify the expression $-x^{2}y + x^{2}y$. 2. Formula and rules: When adding or subtracting like terms, combine their coefficients and keep the variable part unchanged. 3. Intermediate work: $$-x^{2}y + x^{2}y = (-1 + 1) x^{2} y$$ 4. Simplify the coefficients: $$(-1 + 1) = \cancel{-1} + \cancel{1} = 0$$ 5. Final expression: $$0 \times x^{2} y = 0$$ 6. Explanation: Since the two terms are exact opposites, their sum is zero. This is because adding a number and its negative cancels out to zero. Final answer: $0$