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Find the coefficient of the x3y5 term of the expansion (x + y)8.

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By the binomial theorem,


(x+y)^8=\displaystyle\sum_(n=0)^8\binom8nx^(8-n)y^n

The
x^3y^5 term occurs for
n=5; this gives the term


\dbinom85x^(8-5)y^5=(8!)/(5!(8-5)!)x^3y^5=56x^3y^5

so the coefficient is 56.

User Sherlock
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