Factorise \(9a^2-25b^2\).

Correct answer: \((3a-5b)(3a+5b)\)

The direct answer is B: \((3a-5b)(3a+5b)\). First recognise that \(9a^2=(3a)^2\) and \(25b^2=(5b)^2\). Thus the expression has the form \(x^2-y^2\), where \(x=3a\) and \(y=5b\). The difference-of-squares identity is \(x^2-y^2=(x-y)(x+y)\), so \(9a^2-25b^2=(3a-5b)(3a+5b)\). Checking by multiplication gives \(9a^2+15ab-15ab-25b^2=9a^2-25b^2\). A is wrong because \((3a-5b)^2\) produces a middle term \(-30ab\) and a positive \(25b^2\). C does not expand to the given expression. D produces a positive middle term and positive \(25b^2\). Memory cue: a difference of two squares becomes the product of the difference and the sum; it is not the square of one binomial.