We want to find the fifth term of the expansion of the given expression.
(x-4)^9 ⇔ ( x+( -4))^9To 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= x, b= -4, and n= 9. Since k starts at 0, for the fifth term we have k=4. 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.
