Answer to Question #74802 in Combinatorics | Number Theory for nikki

Question

Find the coefficient of x^6 in the expansion of (1-3x)(1+2x)^9 using the general term: t= nCr a^n-r b^r

Answer 1

(1+2x)^9=1+C_9^1 (2x)+C_9^2 (2x)^2+C_9^3 (2x)^3+C_9^4 (2x)^4+C_9^5 (2x)^5+
+C_9^6 (2x)^6+⋯
Coefficient of x^6 in the expansion of (1-3x) (1+2x)^9:
u=C_9^6 (2)^6-3C_9^5 (2)^5=9!/6!3!*64-3 9!/5!4!*32=5376-4032=1344.