%5E2.jpeg "(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.