Which are differences of perfect cubes? Check all that apply.

9a3 - 27

125a12 - 72

216a6 - 27y3

8a15 - 27

225a3 - 216

We are to determine if the given are differences of perfect cubes and in order to do so, we simply have to calculate for the cube root of the terms in the given.

(a) 9a³ - 27 = ((∛9) a) ³ - 3³; NO

(b) 125a¹² - 72 = (5a⁴) ³ - (∛72) ³; NO

(c) 216a⁶ - 27y³ = (6a²) ³ - (3y) ³; YES

(d) 8a¹⁵ - 27 = (2a⁵) ³ - (3) ³; YES

(e) 225a³ - 216 = (15a) ³ - (6) ³; YES

Therefore, the answers are the third, fourth, and fifth choices.