## Expanding (a - 5)²: A Step-by-Step Guide

The expression (a - 5)² represents the square of the binomial (a - 5). To expand this, we use the **FOIL** method, which stands for **First, Outer, Inner, Last**. Here's how it works:

### Step 1: Write the expression in expanded form

(a - 5)² is the same as (a - 5) * (a - 5)

### Step 2: Apply FOIL

**First:**Multiply the first terms of each binomial: a * a = a²**Outer:**Multiply the outer terms of the binomials: a * -5 = -5a**Inner:**Multiply the inner terms of the binomials: -5 * a = -5a**Last:**Multiply the last terms of each binomial: -5 * -5 = 25

### Step 3: Combine like terms

The expanded expression is now: a² - 5a - 5a + 25
Combining the middle terms, we get: **a² - 10a + 25**

### Therefore, the expanded form of (a - 5)² is a² - 10a + 25.

**Important Note:** You can also use the **square of a difference** formula: (a - b)² = a² - 2ab + b². In this case, a = a and b = 5, which leads to the same result: a² - 2(a)(5) + 5² = a² - 10a + 25.

### Understanding the Pattern

Expanding squares of binomials reveals a pattern:

**Square of a sum:**(a + b)² = a² + 2ab + b²**Square of a difference:**(a - b)² = a² - 2ab + b²

This pattern is helpful for quickly expanding similar expressions without using FOIL.