Question

Evaluate the coefficient x^6 in the expansion of (x^2 - 2/7)

Answer 1

The question actually being asked is what is the coefficient of
`x^6` in

`(x^2 - \frac 2 7)^7`

Since

`(x^2)^3=x^6`

we're interested in the
`{7 \choose 3}a^3 b^4` term of the expansion of
`(a+b)^7`

So our term of interest is

`{7 \choose 3} (x^2)^3 (-\frac 2 7)^4 = (7(6)(5))/(3(2)(1)) (2^4)/(7^4) x^6 = (2^4(5))/(7^3) x^6 = (80)/(343) x^6`

Answer:

`\quad (80)/(343)`