First slide

Binomial theorem for positive integral Index

Question

The term contacting $x^{3}$ in the expansion of ${(x - 2 y)}^{7}$ is

Moderate

A

$3^{rd}$
B

$4^{th}$
C

$5^{th}$
D

$6^{th}$

Solution

Given expansion is ${(x - 2 y)}^{7}$

We have general term in the expansion ${(x + a)}^{n}$

$(∴ T_{r + 1} =^{n} C_{r} x^{n - r} {(a)}^{r}$ be the expansion of ${(x + a)}^{n})$

$T_{r + 1} =^{7} C_{r} x^{7 - r} {(- 2 y)}^{r}$

$x^{7 - r}$ compare with $x^{3}$ then

$\Rightarrow x^{7 - r} = x^{3}$

Contains $x^{3}$ it $7 - r = 3$

$∵ r = 4$ .

So $T_{5}$ is the required term.

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