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Question

Find the term independent of x in the expansion of (x3+32x2)10.

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Solution

The (r+1)th term is Tr+1=10Cr(x3)10r(32x2)r
=10Crx10r2310r2.(3)r2rx2r
Tr+1=10Cr3310r2×2rx10r22r ........(i)
The term becomes independent when exponent of x is zero.
10r22r=010r2=2r10r=4r
10=5rr=2
Now, substitute r=2 in equation (i), we get
T3=10C2(3)234.22=10!8!2!×33422
T3=10×92×3×3×3×4
Hence, Independent term, T3=512


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