Question

Find the eighth term in the expansion of (2x - 3y)^14

Answer 1

`- \ ^(14)C_7*(2x)^7*(3y)^7`

Explanation:

Binomial expansion:

(2x - 3y)¹⁴

n = 14 ;

r +1 = 8

r = 7

Co-efficient of the binomial expansion is given by:

`^nC_r= (n !)/((n-r)!r!)\\\\\\^(14)C_7=(14!)/(7!7!)\\\\`

`= (14*13*12*11*10*9*8*7!)/(7*6*5*4*3*2*1* 7!)\\\\\\=(14*13*12*11*10*9*8)/(7*6*5*4*3*2*1)\\\\= 13*11*3*8\\\\= 3432`

Eighth term of the binomial expansion is given by:

`\boxed{\bf T_(r+1) =(-1)^r *^n C_r x^(n-r)*y^r }`

`T_8 = T_(7+1) = (-1) ^(14)C_7 (2x)^(14-7) * 3y^(7)`

`=^(14)C_7 (2x)^7*3y^7`

= -3432 * 128x⁷ *2187y⁷

= - 960,740,352x⁷y⁷