First slide

Binomial theorem for positive integral Index

Question

The coefficient of $x^{5}$ in the expansion of ${(1 + x^{2})}^{5} (1 + x)^{4}$ is

Moderate

A

30
B

40
C

50
D

60

Solution

$\begin{array}{l} {(1 + x^{2})}^{5} (1 + x)^{4} \\ = (1 + 5 x^{2} + 10 x^{4} + \dots) (1 + 4 x + 6 x^{2} + 4 x^{3} + \dots) \end{array}$
$∴$ Coefficient of $x^{5}$ is $(5) (4) + (4) (10) = 60$

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