%5E3-expanded.jpeg "(n+1)^3 Expanded")
(n+1)^3 Expanded
When we expand the cube of the sum of n and 1, we get a polynomial expression that involves various terms of n. In this article, we will explore the expansion of (n+1)^3 and its resulting terms.
The Expansion Formula
To expand (n+1)^3, we can use the general formula for the cube of a sum, which is:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
In our case, we substitute a with n and b with 1, resulting in:
(n+1)^3 = n^3 + 3n^2(1) + 3n(1)^2 + (1)^3
Simplifying the Terms
Now, let's simplify each term in the expansion:
- n^3: This term remains unchanged.
- 3n^2(1): Since 1 is multiplied by n^2, we get 3n^2.
- 3n(1)^2: Again, the 1^2 is equal to 1, so we get 3n.
- (1)^3: The cube of 1 is simply 1.
The Expanded Form
Now, let's combine all the simplified terms to get the final expanded form:
(n+1)^3 = n^3 + 3n^2 + 3n + 1
This is the expanded form of (n+1)^3. We can see that the resulting polynomial expression consists of four terms: the cube of n, the square of n multiplied by 3, n multiplied by 3, and a constant term of 1.
