Question

Find the coefficient of x^8 in the expansion of (x^2-2/x)^7

Answer 1

So, the coefficient of x8 in the given expansion will be 210.

Explanation:

We know,

General term in (x+a)n is given by,

Tr+1=C(n,r)xn−rar

∴ General term in (x2−1x)10 ,

Tr+1=C(10,r)(x2)10−r(−1x)r

⇒Tr+1=(−1)rC(10,r)x20−2rx−r

Now, we have to find the term having coefficient x8.

∴20−2r−r=8⇒r=4

So, T5 will have coefficient x8.

∴T5=(−1)4C(10,4)x8

⇒T5=10⋅9⋅8⋅74⋅3⋅2⋅1x8

⇒T5=210x8