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

Practice Questions

Q1
What is the general term in the expansion of (x + y)^n?
  1. C(n, k)x^k y^(n-k)
  2. C(n, k)x^(n-k) y^k
  3. C(n, k)x^n y^k
  4. C(n, k)x^k y^n

Questions & Step-by-Step Solutions

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.
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