X3y3−5x3y5+9y2−8
find coeifecient

The coefficient is 90.

Step-by-step explanation:

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

x5C2x(5−2)(−3y)2=5×41×2x3(−3y)2

= 10x3×9y2=90x3y2

Hence, the coefficient of x3y2 in (x−3y)5 is 

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