## Expanding (5 + n)³

The expression (5 + n)³ represents the cube of the binomial (5 + n). To expand this expression, we can use the following methods:

### Method 1: Using the Binomial Theorem

The Binomial Theorem provides a general formula for expanding expressions of the form (x + y)ⁿ:

**(x + y)ⁿ = ∑(n choose k) x^(n-k) y^k**

where:

**n choose k**represents the binomial coefficient, calculated as n!/(k!(n-k)!).**k**ranges from 0 to n.

Applying this to our expression (5 + n)³, we get:

**(5 + n)³ = (3 choose 0) 5³ n⁰ + (3 choose 1) 5² n¹ + (3 choose 2) 5¹ n² + (3 choose 3) 5⁰ n³**

Calculating the binomial coefficients and simplifying:

**(5 + n)³ = 125 + 75n + 15n² + n³**

### Method 2: Expanding by Multiplication

We can expand (5 + n)³ by multiplying the expression by itself three times:

**(5 + n)³ = (5 + n) * (5 + n) * (5 + n)**

First, expand the first two terms:

**(5 + n) * (5 + n) = 25 + 10n + n²**

Then, multiply this result by (5 + n):

**(25 + 10n + n²) * (5 + n) = 125 + 50n + 5n² + 25n + 10n² + n³**

Combining like terms, we get:

**(5 + n)³ = 125 + 75n + 15n² + n³**

### Conclusion

Both methods lead to the same result:

**(5 + n)³ = 125 + 75n + 15n² + n³**

This is the expanded form of the expression (5 + n)³, representing the volume of a cube with side length (5 + n).