Disproving an Erroneous Algebraic Identity
Disprove the following algebraic identity: \((a+b)^2 = a^2 + 2ab + b^2 + 2a + 2b\). Provide a specific counterexample where the identity fails.
Disproof by Counterexample: Sum of Two Odds
Prove or disprove: For every pair of odd integers, their sum is always an odd integer. Provide a counterexample if your claim is false.