Question

Find the 6th term in the expanded form of the equation (2x+y)^9

Answer 1

`Use\ the\ Pascal's\ Triangle\ (look\ at\ the\ picture)\\\\6-th\ term\ of\ (2x+y)^9\ is\\\\ 126(2x)^4y^5=126*16x^4y^5=2016x^4y^5`

Answer 2

`T_r={n \choose r-1}a^(n-(r-1))b^(r-1)\\ T_6={9 \choose 6-1}(2x)^(9-(6-1))y^(6-1)\\ T_6={9 \choose 5}(2x)^4y^(5)\\ T_6=(9!)/(5!4!)16x^4y^(5)\\ T_6=(6\cdot7\cdot8\cdot9)/(2\cdot3\cdot4)16x^4y^(5)\\ T_6=7\cdot2\cdot9\cdot16x^4y^(5)\\ T_6=2016x^4y^5`