Use the binomial theorem to write the first three terms.

Question

Quizplus · Accepted Answer

The binomial theorem states that:

(a + b)^n = C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + ... + C(n,n)b^n

where C(n,r) represents the binomial coefficient, or the number of ways to choose r items from a set of n items.

In this case, we have (1 + x)^11, so we can use the binomial theorem to expand it as:

(1 + x)^11 = C(11,0)1^11 + C(11,1)1^10x + C(11,2)1^9x^2 + ...

The first three terms will be:

C(11,0)1^11 = 1
C(11,1)1^10x = 11x
C(11,2)1^9x^2 = 55x^2

Therefore, the answer is choice C.

Use the Binomial Theorem to Write the First Three Terms