Question

Find a constant term in the expansion of (x+(1/x))(x-(2/x))^7

i know that the answer is supposed to be 8 (i think) but i don’t know how to get there

Answer 1

answer: 280

Explanation:

`A(x)=(x+(1)/(x) ){(x-(2)/(x) )}^7=((x^2+1)(x^2-2)^7)/(x^8) \\\\(x^2-2)^7=x^(14)-14*x^(12)+84*x^(10)-280*x^8+560*x^6-672*x^4+448*x^2-128\\\\A(x)=\frac{x^(16)-13*x^(14)+70*x^(12)-196*x^(10)+280*x^8-112*x^6-224*x^4+320*x^2-128 } { x^8 } \\\\`

`constant\ term\ =(280*x^8)/(x^8) =280`