What are the factors of \(x^2-49y^2\)?

Correct answer: \((x-7y)(x+7y)\)

The direct answer is A: \((x-7y)(x+7y)\). Rewrite \(49y^2\) as \((7y)^2\). Then the expression becomes \(x^2-(7y)^2\), a difference of squares. Applying \(u^2-v^2=(u-v)(u+v)\), with \(u=x\) and \(v=7y\), gives \((x-7y)(x+7y)\). Expanding option A gives \(x^2+7xy-7xy-49y^2=x^2-49y^2\); the cross terms cancel. Option B uses 49y rather than 7y as the square-root part and does not expand correctly. Option C is \((x+7y)^2\), which contains the extra term \(+14xy\). Option D is \((x-7y)^2\), which contains \(-14xy\). Since the original has no \(xy\) term, neither square is suitable. Memory cue: difference of squares gives conjugate brackets, not two identical brackets.