Choose the correct factorised form of (16a^2-b^2).

((4a-b)(4a+b))

The expression is a difference of two squares. The identity is \\(A^2-B^2=(A-B)(A+B)\\), which means that each square must first be recognised correctly. Here, \\(16a^2=(4a)^2\\) and \\(b^2=b^2\\). Therefore the two square roots are \\(4a\\) and \\(b\\), so the factors use subtraction and addition of these roots. This idea is different from squaring a difference, because \\((4a-b)^2\\) would also contain a middle term \\(-8ab\\), which is not present.

Applying the identity gives \\(16a^2-b^2=(4a-b)(4a+b)\\). Thus option A is correct. Option B incorrectly treats \\(16a^2\\) as though its linear square root were \\(16a\\), while option C creates a middle term. Option D does not multiply back to the original expression. Careful identification of the square roots is the essential step.

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