Question

I just started learning about using factorial form of the binomial theorem to expand, but my textbook didn't really explain everything well so I'm a bit confused. I was told to find the eighth term of (3a+b)^9. Can someone check my answer? Thanks.

9!
----- 3a^2 (b)^7
(9-7)7!

9 × 8 × 7
---------------- 3a^2 (b)^7
2 × 7

72
------- 3a^2 (b)^7
2

216
-------- a^2 (b)^7
2

108a^2 b^7

Answer 1

9!/(7!2!) = (9*8)/(1*2) = 36 = 9C2
So, the 8th term is
36 (3a)^2 b^7 = 36*9 a^2 b^7 = 324 a^2 b^7

Note that (3a)^2 ≠ 3a^2
it is (3a)(3a) = 9a^2

Answer 2

Thank you so much for your help. I now understand how to do this!!!!