Determine the coefficient of (x^{2}) in the expansion of ((a + 3x)^{6}).

Determine the coefficient of (x^{2}) in the expansion of ((a + 3x)^{6}).

  • A.
    (18a^{2})
  • B.
    (45a^{4})
  • C.
    (135a^{4})
  • D.
    (1215a^{2})
Correct Answer: Option C
Explanation

((a + 3x)^{6}).

The coefficient of (x^{2}) is:

(^{6}C_{4}(a)^{6 – 2} (3x)^{2} = frac{6!}{(6 – 4)! 4!} (a^{4})(9x^{2}))

(15 times a^{4} times 9 = 135a^{4})

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