# Solution to #1-10

Paper 2 Difficulty: Medium

Consider the expansion of $\left ( \frac{1}{3}x – 2 \right ) ^{7}$. Find the coefficient of $x^{3}$.

[Maximum mark: 3]

$a = \frac{1}{3}x, b=-2$ and n=7.

Therefore $\binom{7}{r} \left ( \frac{1}{3}x \right ) ^{7-r} \left ( -2 \right ) ^{r}$.

To find the coefficient of $x^{3}$, we require that r = 4.

So $\binom{7}{4} \left ( \frac{1}{3}x \right ) ^{7-4} \left ( -2 \right ) ^{4} = 20.74x^{3}$ The coefficient of $x^{3}$ is approximately 20.74.