In the expansion of (1 + x)(a - bx)^12, where ab is not equal to
0, the coefficient of x^8 is zero. Find in its simplest form the
value of the ratio a/b.
I expanded (a - bx)^ 12 using binomial theorem. So you get
(+....-729a^5b^7x^7 + 495a^4b^8x^8 ...+)
Now you'll have (1 + x)(+....-729a^5b^7x^7 + 495a^4b^8x^8
...+)
Whe you expand it out, you'll get 495a^4b^8 - 729a^5b^7
= 0. I don't think i made any careless mistakes in the
expansion as I did it numerous times, but somehow or rather, I
still can't derive the answer. It seems awkward (the equation). Or
is there an alternative to solving this question? By the way, you
should get 5/8 in the end.
