We want to find the third term of the expansion of the given expression.
( a+ 2b)^8To do so, we will use the Binomial Theorem to write the expansion in sigma notation.
(a+b)^n=∑_(k=0)^n n!/k!(n-k)!a^(n-k)b^k
For our expression, we have that a= a, b= 2b, and n= 8. Since k starts at 0, for the third term we have k=2. Remember that we do not have to find the sum — we only need to find one of the terms. Therefore, we will only consider the argument of the summation notation instead of the entire sum.
