If \(f(x)=x-1\) and \(g(x)=x+1\), which algebraic identity should be used to simplify \((fg)(x)=f(x)g(x)\)?

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

Here, \((fg)(x)=(x-1)(x+1)\). This matches the identity \((a-b)(a+b)=a^2-b^2\), with \(a=x\) and \(b=1\). Hence, \((fg)(x)=x^2-1\). Options B and D are identities for squaring a binomial, while option C is for the sum of two cubes. Exam tip: when two binomials have opposite signs and the same terms, use the difference-of-squares identity.