Binomial TheoremHard
Question
In the expansion of (x + y + z)25
Options
A.every term is of the form 25Cr. rCk. x25 - r. yr - k. zk
B.the coefficient of x8 y9 z9 is 0
C.the number of terms is 325
D.none of these
Solution
(x + y + z)25
General term
xr1 yr2 xr3
Putting r3 = k, r2 = r - k and r1 = 25 - r
=
× x25-r yr-k zk = 25Cr . rCk . x25-r yr-k zk
r1 + r2 + r3 = 25
∴ coefficient of x8 y9 z9 is 0
General term
xr1 yr2 xr3Putting r3 = k, r2 = r - k and r1 = 25 - r
=
× x25-r yr-k zk = 25Cr . rCk . x25-r yr-k zk r1 + r2 + r3 = 25
∴ coefficient of x8 y9 z9 is 0
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