Answer: 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=5×41×2×3(−3y)2 = 10×3×9y2=90x3y2 Hence, the coefficient of x3y2 in (x−3y)5 is Log in to Reply
Answer:
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=5×41×2×3(−3y)2
= 10×3×9y2=90x3y2
Hence, the coefficient of x3y2 in (x−3y)5 is