which statement about the simplified binomial expansion of (a - b)^n, where a, b and n are positive…

which statement about the simplified binomial expansion of (a - b)^n, where a, b and n are positive integers, is true?\nall terms of the expansion are positive.\nall terms in the expansion are negative.\nthe first term in the expansion is positive.\nthe first term in the expansion is negative.

which statement about the simplified binomial expansion of (a - b)^n, where a, b and n are positive integers, is true?\nall terms of the expansion are positive.\nall terms in the expansion are negative.\nthe first term in the expansion is positive.\nthe first term in the expansion is negative.

Answer

Explanation:

Step1: Recall binomial theorem

The binomial expansion of ((a - b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}(-b)^{k}). The first - term occurs when (k = 0).

Step2: Find the first - term

When (k = 0), the term is (\binom{n}{0}a^{n-0}(-b)^{0}). Since (\binom{n}{0}=1) and ((-b)^{0}=1), the first - term is (a^{n}). Given that (a) is a positive integer and (n) is a positive integer, (a^{n}>0).

Answer:

The first term in the expansion is positive.