The coefficient is 90.
Expansion of (a+b)n gives us (n+1) terms which are given by
binomial expansion xnCra(n−r)br, where r ranges from n to 0.
Note that powers of a and b add up to n and in the given problem this n=5.
In (x−3y)5, we need coefficient of x3y2, we have 3rd power of x and as such r=5−3=2
and as such the desired coefficient of x3y2 is given by
Hence, the coefficient of x3y2 in (x−3y)5 is
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