Which of the following equalities is an algebraic identity for all real values of the variables?

Correct answer: \((a-b)^2=a^2-2ab+b^2\)

Expanding \((a-b)^2=(a-b)(a-b)\) gives \(a^2-ab-ab+b^2=a^2-2ab+b^2\). Hence, option A is true for every real value of \(a\) and \(b\). Option D is the expansion of \((a+b)^2\), while B has the wrong sign for \(b^2\) and C has an incorrect coefficient in the middle term. Exam tip: the middle term in \((x-y)^2\) is always \(-2xy\).