Show that the ratio of the coefficient of x10 in the expansion of (1 – x2)10 and the term independent of x in the expansion of is 1 : 32.

To Prove : coefficient of x10 in (1-x2)10: coefficient of x0 in = 1:32


For (1-x2)10 ,


Here, a=1, b=-x2 and n=15


We have formula,





To get coefficient of x10 we must have,


(x)2r = x10


• 2r = 10


• r = 5


Therefore, coefficient of x10


For ,


Here, a=x, and n=10


We have a formula,







Now, to get coefficient of term independent of xthat is coefficient of x0 we must have,


(x)10-2r = x0


• 10 - 2r = 0


• 2r = 10


• r = 5


Therefore, coefficient of x0


Therefore,





Hence,


coefficient of x10 in (1-x2)10: coefficient of x0 in = 1:32


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