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WAEC Further Mathematics 2011 Paper

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Question : 23

Total: 40

Determine the coefficient of

x^{2}

in the expansion of

(a + 3x)^{6}

.

$18a^{2}$
$45a^{4}$
$135a^{4}$
$1215a^{2}$

Solution:

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

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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