## Expanding the Expression (x + 5)(x + 2)

The expression (x + 5)(x + 2) represents the product of two binomials. To expand this expression, we can use the **FOIL** method, which stands for **First, Outer, Inner, Last**.

Here's how it works:

**1. First:** Multiply the **first** terms of each binomial: x * x = x²

**2. Outer:** Multiply the **outer** terms of the binomials: x * 2 = 2x

**3. Inner:** Multiply the **inner** terms of the binomials: 5 * x = 5x

**4. Last:** Multiply the **last** terms of each binomial: 5 * 2 = 10

Now we have: x² + 2x + 5x + 10

Finally, combine the like terms:

**x² + 7x + 10**

Therefore, the expanded form of (x + 5)(x + 2) is **x² + 7x + 10**.

### Why is the FOIL Method Useful?

The FOIL method provides a systematic way to multiply binomials, ensuring that all terms are accounted for. It helps us to avoid mistakes and simplifies the process of expansion.

### Applications of Expanding Binomials

Expanding binomials is a fundamental concept in algebra with various applications, including:

**Solving quadratic equations:**By factoring a quadratic equation into two binomials, we can easily find its roots.**Graphing quadratic functions:**Expanding the expression helps us determine the vertex, axis of symmetry, and other key features of the parabola.**Simplifying expressions:**Expanding binomials can help simplify complex expressions and make them easier to work with.

By understanding the process of expanding binomials, we gain a deeper understanding of algebraic operations and their applications in various mathematical contexts.