%5E2.jpeg "(a-5)^2")
Expanding (a - 5)²: A Step-by-Step Guide
The expression (a - 5)² represents the square of the binomial (a - 5). To expand this, we use the FOIL method, which stands for First, Outer, Inner, Last. Here's how it works:
Step 1: Write the expression in expanded form
(a - 5)² is the same as (a - 5) * (a - 5)
Step 2: Apply FOIL
- First: Multiply the first terms of each binomial: a * a = a²
- Outer: Multiply the outer terms of the binomials: a * -5 = -5a
- Inner: Multiply the inner terms of the binomials: -5 * a = -5a
- Last: Multiply the last terms of each binomial: -5 * -5 = 25
Step 3: Combine like terms
The expanded expression is now: a² - 5a - 5a + 25 Combining the middle terms, we get: a² - 10a + 25
Therefore, the expanded form of (a - 5)² is a² - 10a + 25.
Important Note: You can also use the square of a difference formula: (a - b)² = a² - 2ab + b². In this case, a = a and b = 5, which leads to the same result: a² - 2(a)(5) + 5² = a² - 10a + 25.
Understanding the Pattern
Expanding squares of binomials reveals a pattern:
- Square of a sum: (a + b)² = a² + 2ab + b²
- Square of a difference: (a - b)² = a² - 2ab + b²
This pattern is helpful for quickly expanding similar expressions without using FOIL.