Which is the correct factorisation of (x² - 16)?

Correct answer: (x - 4)(x + 4)

Answer: D, (x - 4)(x + 4). Since 16 = 4², the expression can be written as x² - 4². It is therefore a difference of two squares. Using a² - b² = (a - b)(a + b), with a = x and b = 4, we obtain x² - 16 = (x - 4)(x + 4). Option A incorrectly uses 16 instead of its square root, 4, as the second number. Option B expands to x² - 8x + 16, which has a middle term. Option C expands to x² + 8x + 16, also with a middle term and a different sign. Multiplying option D confirms the result: x² + 4x - 4x - 16 = x² - 16. Memory cue: take the square root of the constant before forming the two factors.