## Expanding (x+5)(x+5)

This expression represents the product of two identical binomials, (x+5) and (x+5). We can expand it using 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 * 5 = 5x

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

**4. Last:** Multiply the **last** terms of each binomial:
5 * 5 = 25

**5. Combine Like Terms:** Now, add all the terms together:
x² + 5x + 5x + 25 = **x² + 10x + 25**

Therefore, the expanded form of (x+5)(x+5) is **x² + 10x + 25**.

### Understanding the Result

The expanded form represents a **quadratic expression**, which is a polynomial with the highest power of the variable being 2. It can be visualized as a parabola when graphed.

This specific expression, **x² + 10x + 25**, is a **perfect square trinomial**. This means it can be factored back into the original form, (x+5)(x+5).

### Applications

Expanding binomials like (x+5)(x+5) is essential in various mathematical contexts, including:

**Algebraic manipulation:**Simplifying expressions, solving equations, and working with polynomials.**Calculus:**Finding derivatives and integrals.**Geometry:**Calculating areas and volumes.**Physics and engineering:**Modeling real-world phenomena.

Understanding how to expand binomials is a fundamental skill in mathematics.