%5E2-standard-form.jpeg "(a-5)^2 Standard Form")
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):
- First terms: a * a = a²
- Outer terms: a * -5 = -5a
- Inner terms: -5 * a = -5a
- Last 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.