Find the specified nth term in the expansion of the binomial.

Question

Equation: (x – 10z)⁷, n = 3

Answer 1

x^7 + (7)(x^6)(-10z)^6 + 21(x^5)(-10z)^2 are the 1st three terms of the expansion

that 3rd term is 2100x^5z^2

the first three coefficents are combinations, (7/7) = 7!/7!0! = 1 (7/6) = 7!/6!1! =7 and (7/5) = 7!/5!2!= 42/2 = 21

the 3rd term is (7/5)(x^5)(-10z)^5 = 7!/5!2!(x^5)(-10z^2) = 2100x^5z^2