Factorise (16a^2-24ab+9b^2-25c^2).

Correct answer: ((4a-3b-5c)(4a-3b+5c))

The first three terms form a perfect square. Since \((4a)^2=16a^2\), \((3b)^2=9b^2\), and the middle term of \((4a−3b)^2\) is \(−2(4a)(3b)=−24ab\), we have \(16a^2−24ab+9b^2=(4a−3b)^2\). Also, \(25c^2=(5c)^2\). The expression is therefore \((4a−3b)^2−(5c)^2\). Applying the difference-of-squares identity gives \((4a−3b−5c)(4a−3b+5c)\), option A.

Multiplying these factors confirms the answer because they are conjugates: their product is \((4a−3b)^2−25c^2\), exactly the original expression. The plus sign between 4a and 3b would produce a positive \(24ab\) term, so option B cannot work. Option D lacks the subtraction of \(25c^2\), and option C does not follow from either a common factor or a standard identity.