Question

Using binomial find the coefficient of x^6 in the expansion (1/x^2-x) ^18​

Answer 1

Answer:

2 is a the answer for given question

Answer 2

Answer:

Put u=x2 , the expression becomes P(u)=2−6u−3(u+1)(u–8)6 . Then the coefficient of x2 is the coefficient of u . To find it, at first need to see the term of 4th -degree in (u+1)(u−8)6 .

In the expansion of (u−8)6(u+1) , we observe that (u+1)(…+a4u4+a3u3+…)=…+(a4+a3)u4+… . Thus the coefficient of the 4th -degree term equals −83⋅6!/3!⋅3!+82⋅6!/2!⋅4!

Now divide it to 2−6 we get the coefficient of u in P(u) , which is −145 .