What is the factorised form of 36p² − 49q²?

Correct answer: (6p − 7q)(6p + 7q)

The direct answer is D: (6p − 7q)(6p + 7q). Recognise 36p² − 49q² as a difference of two squares. Since 36p² = (6p)² and 49q² = (7q)², apply A² − B² = (A − B)(A + B). Thus 36p² − 49q² = (6p)² − (7q)² = (6p − 7q)(6p + 7q). Multiplying the two factors gives (6p)² − (7q)², because the cross terms cancel. Option A uses 36p and 49q instead of their square roots, so it is much too large and expands incorrectly. Option B is a square of a difference and would create a middle term −84pq. Option C does not use matching square roots and cannot produce the given terms. Option D is correct because it has the same two square roots and opposite signs. A useful cue is: subtraction between two perfect squares leads to conjugate factors.