What is the complete factorised form of 2a² − 8b²?

Correct answer: 2(a − 2b)(a + 2b)

The direct answer is A: 2(a − 2b)(a + 2b). First identify the greatest common factor of 2a² and 8b², which is 2. Taking it out gives 2(a² − 4b²). The expression inside is a difference of squares because 4b² = (2b)². Use a² − c² = (a − c)(a + c): a² − (2b)² = (a − 2b)(a + 2b). Thus the complete factorisation is 2(a − 2b)(a + 2b). Option A expands back to 2(a² − 4b²) = 2a² − 8b². Option B would give 2(a² − b²), whose second term is −2b², not −8b². Option C does not produce the required terms when multiplied. Option D represents a square, but the original expression is a difference of squares, not a repeated square. Memory cue: take out a common factor before applying an identity.