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

Correct answer: (4a-b)(4a+b)

The direct answer is A: \((4a-b)(4a+b)\). Recognise the expression as a difference of two squares. Since \(16a^2=(4a)^2\) and \(b^2=b^2\), the two square roots are \(4a\) and \(b\). Apply \(P^2-Q^2=(P-Q)(P+Q)\): \(16a^2-b^2=(4a-b)(4a+b)\). Expanding gives \(16a^2+4ab-4ab-b^2=16a^2-b^2\), so the result is verified. B treats \(16a\) as the square root of \(16a^2\), but the correct square root is \(4a\); its expansion would be \(256a^2-b^2\). C is a square of a difference and would produce the extra middle term \(-8ab\). D expands to \(16a^2+6ab-b^2\), so it is not equal to the original expression. Always find the actual square roots before applying the identity.