Question

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

Answer 1

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.