Which identity is useful to calculate \( 103\times97 \)?

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

Here, \(103=100+3\) and \(97=100-3\). Thus the product is of the form \((100+3)(100-3)\), so we use \((a+b)(a-b)=a^2-b^2\). Hence, \(103\times97=100^2-3^2=10000-9=9991\). The identity \((a-b)^2\) is for the square of one binomial, so it does not fit here. Exam tip: when two numbers are equally spaced from the same number, look for the difference-of-squares identity.