Find the coefficient of $x^{18}$ in ${(a x^{4} - b x)}^{9}$ .

Open in App

Solution

Let's write it as $x^{9} (a x^{3} - b)$ , general term in its expansion will be $^{n} C_{r} x^{9} (a x^{3})^{r} (- b)^{n - r}$ where r varies from 0 to n.
Power of $x$ is $18$ $\Rightarrow 9 + 3 r = 18$
$\Rightarrow r = 3$
Coefficient of $x^{18} =^{9} C_{3} a^{3} b^{6} = 84 a^{3} b^{6}$

Suggest Corrections

Similar questions

x^{18}

{(x^{2} + \frac{3 a}{x})}^{15}

x^{18}

{(x^{2} + \frac{3 a}{x})}^{15}

x^{18}

(1 + x) (1 - x)^{10} (1 + x + x^{2})^{9}

(2 r + 3)^{t h}

(r - 1)^{t h}

{(1 + x)}^{18}

r

r

(2 r + 4)^{t h}

(r - 2)^{t h}

(1 + x)^{18}

Join BYJU'S Learning Program