What is the factorised form of 16n² − 25?

Correct answer: (4n − 5)(4n + 5)

The correct answer is A: (4n − 5)(4n + 5). Recognise 16n² − 25 as a difference of two squares. Since 16n² = (4n)² and 25 = 5², use the identity a² − b² = (a − b)(a + b). Substitution gives (4n)² − 5² = (4n − 5)(4n + 5). Expanding this answer gives 16n² + 20n − 20n − 25 = 16n² − 25, so it is verified. Option B is a square of a binomial and would contain a middle term −40n. Option C incorrectly uses 16n instead of its square root 4n, producing 256n² − 25. Option D has n rather than 4n and produces n² − 25. Memory cue: in a difference of squares, take the square root of each term before making the two brackets.