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

The expression (a - 5)² represents the square of the binomial (a - 5). To write it in standard form, we need to expand and simplify the expression.

### Understanding the Problem:

**Standard form of a quadratic expression:**ax² + bx + c, where a, b, and c are constants.**Binomial:**An algebraic expression with two terms (e.g., (a - 5)).**Squaring a binomial:**Multiplying the binomial by itself.

### Expanding the Expression:

**Rewrite the expression:**(a - 5)² = (a - 5)(a - 5)**Apply the distributive property (FOIL method):****F**irst terms: a * a = a²**O**uter terms: a * -5 = -5a**I**nner terms: -5 * a = -5a**L**ast terms: -5 * -5 = 25

**Combine the terms:**a² - 5a - 5a + 25

### Simplifying the Expression:

**Combine like terms:**a² - 10a + 25

### The Final Result:

The standard form of (a - 5)² is **a² - 10a + 25**.

### Key Points:

**Remember the FOIL method:**It's a useful tool for expanding binomials.**Combine like terms:**Simplify the expression after expansion.**Standard form:**Always present the final result in the standard form of a quadratic expression.