Find the coefficient of the term containing y ^9 in the expansion of (−x + 2y) ^12 .

Answer 1

∑ⁿ_i=0(ⁿ_i)(a^n-i)bⁱ

where a = -x, b = 2y, n = 12 and the term where i = 9 gives y⁹_.

_{The binomial coefficient, 12 things taken 9 at a time), is equivalent to 12 things taken 3 at a time = 12(11)(10)/3! = 220.}

_{So the 10 term of (-x + 2y)}¹² _equals:

_{220 (-x)}^(12-9)_(2y)⁹ _{= 220(-x}³₎₍₂⁹_)x⁹_{= -112640x}³_y⁹.

The numerical coefficient of that term: -112640.