Determine the coefficient of x^5 in the binomial expansion of (2-3x)^7?
(2-3x)^7
= 2^7 + C(7,1)(2^6)(-3x) + C(7,2)(2^5)(-3x)^2 +...+ C(7,5)(2^2)(-3x)^5 + ...
so we want C(7,5)(2^2)(-3x)^5
= 21(4)(-243)x^5
= - 20412x^5
check my arithmetic
= 2^7 + C(7,1)(2^6)(-3x) + C(7,2)(2^5)(-3x)^2 +...+ C(7,5)(2^2)(-3x)^5 + ...
so we want C(7,5)(2^2)(-3x)^5
= 21(4)(-243)x^5
= - 20412x^5
check my arithmetic