(a-5)^2

2 min read Jun 16, 2024
(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.

Related Post


Featured Posts