find the 8th term of (x+3y)^10?

Question

what does it mean the 8th term?
can someone please explain how to solve the problem?
=) thank you!

Answer 1

It's C(10,7) * x^3 * (3y)^7
= 262,440 x^3 y^7

Answer 2

Each term will have the form:

C(n)* x^(10-n)*(3y)^n
for n=0 to 10

C(n) is a value given by Pascal's triangle (line 10) or by finding the factor:
C(n) = 10 factorial / [n factorial times (10-n) fatorial]

Careful: first term, n=0
second term, n=1

eighth term, n=7

(there are 11 terms in the 10th power expansion)

120*x^3*(3y)^7
120*3^7*x^3*y^7
262,440*x^3*y^7

This is a rewrite, as I got it backwards the first time around (used x^7 and (3y)^3 )

Answer 3

the formula of the general term is C_n^k * a^n-k * b^k

so in your exercise a from the formula is x b is 3y n is 10 and k is 7(you want the 8th term so we put minus one)

so we have now c_10^7 * x^3 * 3y^7