Write (36a^2-b^2) in factors.

Correct answer: (6a-b)(6a+b)

The direct answer is A: \((6a-b)(6a+b)\). Begin by noticing that \(36a^2=(6a)^2\) and \(b^2=b^2\). Thus the expression has the form \(U^2-V^2\), called a difference of two squares. The identity is \(U^2-V^2=(U-V)(U+V)\). Taking \(U=6a\) and \(V=b\) gives \(36a^2-b^2=(6a-b)(6a+b)\). To check A, multiply: \((6a-b)(6a+b)=36a^2+6ab-6ab-b^2=36a^2-b^2\); the middle terms cancel. B expands to \(36a^2+36ab-ab-b^2\), which is not the original expression. C expands to \(36a^2+12ab+b^2\), so both the middle and last signs are wrong. D expands to \(36a^2-12ab+b^2\), also incorrect. A common confusion is to use a square such as \((6a-b)^2\); that creates a middle term. In a difference of squares, the two factors have opposite signs between their corresponding terms.