find the fourth term of the binomial expansion (a-5)^7
To find the fourth term of the binomial expansion (a-5)^7, we can use the binomial theorem formula:
The formula for the fourth term (kth term) of the binomial expansion (a+b)^n is given by:
Term(k) = (nCk) * (a^(n-k)) * (b^k)
In this case, a = a, b = -5, and n = 7.
Term(4) = (7C4) * (a^(7-4)) * ((-5)^4)
Using combinatorial notation, 7C4 = 7! / (4! * (7-4)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
So, Term(4) = 35 * (a^3) * (-5^4)
Simplifying, (-5^4) = (-5 * -5 * -5 * -5) = 625
Thus, Term(4) = 35 * (a^3) * 625 = 21875a^3.
Therefore, the fourth term of the binomial expansion (a-5)^7 is 21875a^3.