What is the factorised form of (7x^2-28xy)?

Correct answer: (7x(x-4y))

The direct answer is A: the factorised form is \(7x(x-4y)\). Factorisation means writing an expression as a product of simpler factors. In \(7x^2-28xy\), the first term is \(7x\cdot x\), and the second term is \(7x\cdot(-4y)\). Therefore, taking the common factor \(7x\) outside gives \(7x(x-4y)\). Multiplying back confirms it: \(7x\cdot x=7x^2\) and \(7x\cdot(-4y)=-28xy\). Option A is correct because both the number 7 and the variable x have been taken out. Option B, \(7(x^2-4y)\), is wrong because multiplying it gives \(7x^2-28y\), which lacks x in the second term. Option C, \(x(7x-28)\), gives \(7x^2-28x\), not \(-28xy\); the y has disappeared. Option D, \(7xy(x-4)\), gives \(7x^2y-28xy\), adding an unwanted y to the first term. A useful exam cue is to find the greatest common factor of every term and then check by multiplication.