If the expansion of (x² + 6x + 9)³ⁿ has 13 terms, what is n?

Correct answer: b 2

(x² + 6x + 9) = (x + 3)², so the expression is (x + 3)⁶ⁿ with 6n + 1 = 13, n = 2, so this is the value.

Why the other options are wrong

• a 3: n = 3 gives 19 terms. The right answer is 2.
• c 1: n = 1 gives 7 terms. The right answer is 2.
• d −2: n = −2 makes the power negative, so the number of terms is meaningless. The right answer is 2.