## Understanding the Expansion of (a + b)(a² - ab + b²)

The expression (a + b)(a² - ab + b²) is a special case of polynomial multiplication that results in a very important formula. Let's break it down step-by-step:

### The Concept

This expression represents the multiplication of two binomials:

**(a + b):**The first binomial, containing two terms: 'a' and 'b'.**(a² - ab + b²):**The second binomial, containing three terms: 'a²', '-ab', and 'b²'.

To expand this, we'll use the distributive property of multiplication.

### The Expansion

We can expand the expression by multiplying each term in the first binomial with every term in the second binomial:

**a(a² - ab + b²) = a³ - a²b + ab²****b(a² - ab + b²) = a²b - ab² + b³**

Now, combining the results:

**(a + b)(a² - ab + b²) = a³ - a²b + ab² + a²b - ab² + b³**

Notice that the terms **-a²b** and **a²b**, and **ab²** and **-ab²** cancel each other out.

### The Result

This leaves us with the simplified form:

**(a + b)(a² - ab + b²) = a³ + b³**

### Significance of the Formula

This formula is known as the **sum of cubes** formula. It provides a simple way to factorize expressions in the form of a³ + b³, and it has applications in various areas of mathematics, including algebra, trigonometry, and calculus.

**In Summary:**

The expansion of (a + b)(a² - ab + b²) demonstrates the power of distributive property and leads to the important sum of cubes formula: **a³ + b³**. This formula provides a crucial tool for simplifying and factoring expressions, contributing to a deeper understanding of mathematical concepts.