What is the general term in the expansion of (x + y)^n?

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Question: What is the general term in the expansion of (x + y)^n?

Options:

Correct Answer: C(n, k)x^k y^(n-k)

Solution:

The general term in the expansion of (x + y)^n is given by C(n, k)x^k y^(n-k).

What is the general term in the expansion of (x + y)^n?

What is the general term in the expansion of (x + y)^n?

Step 1: Understand that (x + y)^n means you are multiplying (x + y) by itself n times.
Step 2: Recognize that in the expansion, each term will have a combination of x's and y's.
Step 3: Identify that the general term is represented as C(n, k)x^k y^(n-k).
Step 4: Learn what C(n, k) means: it is the number of ways to choose k items from n items, also known as 'n choose k'.
Step 5: Realize that k can be any integer from 0 to n, which gives you different terms in the expansion.
Step 6: Understand that x^k means you have x multiplied by itself k times, and y^(n-k) means you have y multiplied by itself (n-k) times.

No concepts available.