(a-8)^2

2 min read Jun 16, 2024
(a-8)^2

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:

  • First: a * a = a^2
  • Outer: a * -8 = -8a
  • Inner: -8 * a = -8a
  • Last: -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.

Related Post