## Expanding (x + 1)³

The expression (x + 1)³ represents the cube of the binomial (x + 1). To understand this, we need to expand the expression, which means multiplying it by itself three times:

(x + 1)³ = (x + 1) * (x + 1) * (x + 1)

**Expanding the expression**

We can expand this using the distributive property (often called FOIL for first, outer, inner, last) multiple times:

**First Expansion:**(x + 1) * (x + 1) = x² + 2x + 1**Second Expansion:**(x² + 2x + 1) * (x + 1) = x³ + 2x² + x + x² + 2x + 1**Simplifying:**x³ + 3x² + 3x + 1

Therefore, the expanded form of (x + 1)³ is **x³ + 3x² + 3x + 1**.

**Understanding the Pattern**

The coefficients of the expanded form (1, 3, 3, 1) follow a pattern known as Pascal's Triangle. This triangle is a visual representation of binomial coefficients, where each number is the sum of the two numbers directly above it.

**Applications**

Understanding the expansion of (x + 1)³ has applications in various fields like:

**Algebra:**Solving equations, simplifying expressions, and understanding polynomial behavior.**Calculus:**Finding derivatives and integrals of polynomial functions.**Probability:**Calculating probabilities in binomial distributions.

**Conclusion**

Expanding (x + 1)³ is a fundamental concept in algebra with various applications. By understanding the expansion process and the pattern of coefficients, we can efficiently work with this expression and its applications.