Question

Find the fifth term in the expansion of
$\rm \bigg(x^{2}-\frac{4}{x^{3}}\bigg)^{11}$

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$T_{5}=84480(x^{2})$

Step-by-step explanation:

In the given binomial equation,

$(x^{2}-\frac{4}{x^{3}})^{11}$

We know that the rth term in the expansion of the binomial term of the form (ax + b)ⁿ is given by,

$T_{r}=^{n}C_{r-1}(ax)^{n-(r-1)}(b)^{(r-1)}$

where,

$T_{r}$ is the rth term.

So,

Using the same formula for the rth term we get,

$T_{5}=^{11}C_{5-1}(x^{2})^{11-(5-1)}(\frac{-4}{x^{3}})^{(5-1)}\\T_{5}=^{11}C_{4}(x^{2})^{7}(\frac{-4}{x^{3}})^{4}\\T_{5}=\frac{11!}{4!7!}(x^{2})^{7}(\frac{-4}{x^{3}})^{4}\\T_{5}=\frac{11\times 10\times 9\times 8}{4\times 3\times 2}(x^{14})(\frac{256}{x^{12}})\\T_{5}=330(x^{2})(256)\\T_{5}=84480(x^{2})$

Therefore, the 5th term in the expansion is given by,

$T_{5}=84480(x^{2})$