Which is the factorisation of (16a^2-40ab+25b^2)?

( (4a-5b)^2 )

The expression has the form of a perfect-square identity: \\(a^2-2ab+b^2=(a-b)^2\\). The first term, 16a², is the square of 4a, and the last term, 25b², is the square of 5b. Their middle product is \\(2(4a)(5b)=40ab\\), and the given middle term is 40ab. Therefore the expression is \\( (4a-5b)^2\\), so option B is correct. The negative sign in the middle term is the key clue.

Verification by expansion gives \\( (4a-5b)^2=(4a)^2-2(4a)(5b)+(5b)^2=16a^2-40ab+25b^2\\). The plus-square option would produce a positive middle term, not a negative one. Option C does not use the square roots of the first and last terms correctly, and option D represents a difference of squares, which would remove the middle term instead of producing 40ab. Thus the perfect-square form is unambiguous.

This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.