First slide

Binomial theorem for positive integral Index

Question

The coefficient of x⁵ in the expansion of ${(1 + x^{2})}^{5} (1 + x)^{4}$ is

Moderate

A

40
B

50
C

-50
D

60

Solution

We have, ${(1 + x^{2})}^{5} (1 + x)^{4}$
$\begin{aligned} = (1 +^{5} C_{1} x^{2} +^{5} C_{2} x^{4} + \dots) (1 +^{4} C_{1} x +^{4} C_{2} x^{2} +^{4} C_{3} x^{3} +^{4} C_{4} x^{4}) \\ = (1 + 5 x^{2} + 10 x^{4} + \dots) (1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}) \end{aligned}$
The term giving x5 in the above product is
$(5 x^{2}) (4 x^{3}) + (10 x^{4}) (4 x) = (20 + 40) x^{5} = 60 x^{5}$
Hence, the coefficient is 60.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App