How do you find the 10th term of #(x+3)^12#?

Question

6565 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-03T01:33:14

The tenth term is #4,330,260x^3#.

The nth term in the expansion of #(a + b)^m# is given by #t_(k+ 1)= color(white)(2)_nC_k xx a^(n - k) xx b^k#.

We want to find the 10th term, but we need to find the value of #k# to calculate it. Hence,

#k + 1 = 10#

#k = 9#

#t_10 = color(white)(2)_12C_9 xx x^(12 - 9) xx 3^9#

#t_10 = 220x^3(19,683)#

#t_10 = 4,330,260x^3#

Hopefully this helps!