WAEC - Further Mathematics (2011 - No. 23)
Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).
\(18a^{2}\)
\(45a^{4}\)
\(135a^{4}\)
\(1215a^{2}\)
Vysvetlenie
\((a + 3x)^{6}\).
The coefficient of \(x^{2}\) is:
\(^{6}C_{4}(a)^{6 - 2} (3x)^{2} = \frac{6!}{(6 - 4)! 4!} (a^{4})(9x^{2})\)
\(15 \times a^{4} \times 9 = 135a^{4}\)