## Understanding (a - 8)^2

In mathematics, **(a - 8)^2** represents the square of the binomial expression (a - 8). This means we are multiplying the expression by itself:

**(a - 8)^2 = (a - 8)(a - 8)**

To expand this expression, we can use the **FOIL method**:

**F**irst: a * a =**a^2****O**uter: a * -8 =**-8a****I**nner: -8 * a =**-8a****L**ast: -8 * -8 =**64**

Combining the terms, we get:

**(a - 8)^2 = a^2 - 8a - 8a + 64**

Simplifying further:

**(a - 8)^2 = a^2 - 16a + 64**

### Key Takeaways

**(a - 8)^2**is a perfect square trinomial.- This means it can be factored back into the form (a - 8)(a - 8)
- Expanding the expression using the FOIL method helps us understand how the terms interact and leads to the simplified form.

### Applications

Understanding the expansion of **(a - 8)^2** has applications in various areas of mathematics, including:

**Algebraic manipulations:**This knowledge helps simplify expressions and solve equations.**Quadratic equations:**Perfect square trinomials are commonly encountered in quadratic equations, which can be solved using the quadratic formula or factoring methods.**Calculus:**Understanding how to expand binomials is crucial in calculus when dealing with derivatives and integrals.

By understanding the expansion of **(a - 8)^2**, we gain a fundamental tool in our mathematical toolbox, allowing us to handle more complex expressions and solve a wide range of problems.