Question

Find the coefficient of the fifth term in the expansion(rootK+3)^8

Answer 1

This is the way I remember it. Of course, you can use the formula (given there also), but jotting down the triangle is easy, and counting to row 8 is very easy. http://ptri1.tripod.com/#made

Answer 2

for (a+b)^n

term_r+1 = C(n,r) a^(n-r) b^r

so for (√k + 3)^8
term(5) = C(8,4) (√k)^4 3^4
= 70 k^2 (81)
= 5670k^2

so the coefficient is 5670