Consider the following expression: (1 + x)^n. a) use the binomial theorem to find the first four terms of this polynomial. b) why is 1 + nx a good approximation of this expression when x is less than 1?

Given:

The expression:  (1 + x)^n

The Binomial Theorem is used to predict the products of a binomial raised to a certain power, n, without multiplying the terms one by one. 

The following formula is used:

(a + b)^n = nCk * a^(n-k) * b^k

we have (1 +x)^n,

where a = 1 
            b = x
let n = 4

First term, k = 1

4C1 = 4

first term: 4*(1^(4-1))*x^1

Therefore, the first term is 4x. Do the same for the next three terms. 

2nd term: k =2 
3rd term: k = 3
4th term: k = 4