Question

Find the fifth term of (2x + y)^10

Answer 1

5th term in the expansion is

C(10,4) (2x)^(10-4) (y)^4

= 10C4 (2x)^6 y^4
= 10! / (6! 4! ) 2^6 x^6 y^4
= 7 * 8 * 9 * 10 / 24 * 64 *x^6 y^4
= 13440 x^6 y^4

Answer 2

`T_r={n \choose r-1}a^(n-(r-1))b^(r-1)\\T_5={10 \choose 5-1}(2x)^(10-(5-1))y^(5-1)\\T_5={10 \choose 4}(2x)^6y^(4)\\T_5=(10!)/(4!6!)64x^6y^(4)\\T_5=(7\cdot8\cdot9\cdot10)/(2\cdot3\cdot4)64x^6y^(4)\\T_5=7\cdot3\cdot10\cdot64x^6y^(4)\\T_5=13440x^6y^4`