Write 4r² − 81 in factors.

Correct answer: (2r − 9)(2r + 9)

The direct answer is A: (2r − 9)(2r + 9). First identify the two perfect squares: 4r² = (2r)² and 81 = 9². Thus, 4r² − 81 = (2r)² − 9². Apply the difference-of-squares identity a² − b² = (a − b)(a + b), giving (2r − 9)(2r + 9). Option A can be checked by multiplication: the cross terms are +18r and −18r, so they cancel, leaving 4r² − 81. Option B is incorrect because (2r − 9)² = 4r² − 36r + 81; it has a middle term and a positive constant. Option C does not reproduce the original expression; multiplying it gives 4r² + 27r − 81. Option D expands to 4r² + 36r + 81, so both the middle term and the sign of the constant are wrong. The important distinction is that a difference of two squares produces two conjugate factors, one with subtraction and one with addition. Memory cue: minus between perfect squares means “minus factor, plus factor.”