There is a lazy method:
U can convert the above to
( (x-1)(x-2) ) ^ 4
which gives u
( (x-1)^4 )( (x-2)^4 )
in which u can expand easily to
(x^4 - 4x^3 + 6x^2 - 4x + 1) (x^4 - 8x^3 + 24x^2 - 32x + 16)
note that for the first 3 terms, u will get
a x^8 + b x^7 + c x^6 + ...
coefficient of x^8 will thus be the coefficient of the x^4 (from
the 1st bracket) multiplied by the coefficient of x^4 (from the 2nd
bracket) = 1
similarly, b = (1 * -
+ (-4 * 1) = -12
and c = (1 * 24) + (-4 * - + (6 * 4) = 80
Hence, the first 3 terms are
x^8 - 12x^7 + 80x^6
I may have some careless mistakes in calculations, but the general
lazy way is like above...
Hope it helps.
