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  4. The coefficient of x4 in the expansion of (1 - 2x)5 is equal to

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Q. The coefficient of $x^4$ in the expansion of $(1 - 2x)^5$ is equal to

KEAMKEAM 2017Binomial Theorem

Solution:

General term of $(1-2 x)^{5}$ is given by
$T_{r+1} ={ }^{5} C_{r}(-2 x)^{r} $
$={ }^{5} C_{r}(-2)^{r} X^{r}$
For coefficient of $x^{4}$, power of $X=4$
$\therefore r=4$
$\therefore $ Coefficient of $x^{4}={ }^{5} C_{4}(-2)^{4}$
$=5 \times 16=80$