The absolute difference of the coefficients of x 10 and x 7 in the expansion of 
is equal to
Text Solution
Verified by ExpertsD
The given expansion is 
The general term in the binomial expansion of (x + a) n is given by T r+1 = n C r x n-r a r .
Now for coefficient of x 7 
22 - 3r = 7
r = 5
Coefficient of x 7 is n C 5 (2 n-5x2 )
Now for coefficient of x 10 
22 - 3r = 10
r = 4
Coefficient of x 10 is 11 C 4 (2 11-2x4 )
We need the absolute difference, we get it by | 11 C 5 (2 11-5x2 )- 11 C 4 (2 11-4x2 ) |.
= |924-2640|=1716
= 12 3 - 12
Hence the absolute difference is = 12 3 - 12.
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