Which is the correct factorisation of a² − b²?

Correct answer: (a − b)(a + b)

Answer: A, (a − b)(a + b). The expression a² − b² is called a difference of two squares because a² and b² are squares joined by a minus sign. The identity for this pattern is x² − y² = (x − y)(x + y). Put x = a and y = b; therefore a² − b² = (a − b)(a + b). We can verify it by multiplication: (a − b)(a + b) = a² + ab − ab − b² = a² − b², because the middle terms cancel. Option A is correct. Option B gives (a − b)² = a² − 2ab + b², which has a middle term and a positive b². Option C gives a² + 2ab + b², so both the middle term and the sign pattern are different. Option D gives a² − ab, not the required expression. Memory cue: difference of squares means difference factor times sum factor; never square only one binomial.