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Question

Find the number of integral terms in the expansion of (3+85)256


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Solution

Tr+1=256Cr(3)256r5r8
=256Cr(3)256r25r8
For this term to be an integer, both 256r2 and r8i.e(128r2 and r8) should be integers. r should be a multiple of 8 for r8 to be an integer. When r is a multiple of 8, 128 - r2 (r<257) will also be an integer.
r can take the values 0,8,16.....256
or 0,1×8,2×8,3×8.......32×8
Number of values r can take = 32+1= 33


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