First slide

Binomial theorem for positive integral Index

Question

The coefficient of x in the expansion of $(1 - 3 x + 7 x^{2}) (1 - x)^{16}$ is

Moderate

A

19
B

-19
C

18
D

-18

Solution

$\begin{array}{l} (1 - 3 x + 7 x^{2}) (1 - x)^{16} \\ = (1 - 3 x + 7 x^{2}) (^{16} C_{0} -^{16} C_{1} x +^{16} C_{2} x^{2} + \dots) \end{array}$
After multiplying, the term containing x is
$^{16} C_{1} x - 3 x^{16} C_{0} x$
$∴ Coefficient of x = - 16 - 3 = - 19$

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