Choose the factorised form of (x^2-4y^2+2x+1).

Correct answer: \((x+1-2y)(x+1+2y)\)

The expression can be rearranged as \(x^2+2x+1-4y^2\). Here, \(x^2+2x+1=(x+1)^2\) and \(4y^2=(2y)^2\). Therefore, it is \((x+1)^2-(2y)^2\). Applying the identity \(a^2-b^2=(a-b)(a+b)\) gives \((x+1-2y)(x+1+2y)\). Option B would contain \((x-1)^2\), which gives a \(-2x\) term instead of the required \(+2x\) term. Exam tip: rearrange the expression to spot perfect squares before applying the difference of squares identity.