Difference of Squares

The difference of squares is a special algebraic formula that arises when we have the difference between two perfect square numbers. The general form of the difference of squares is:

a² - b² = (a + b)(a - b)

How to Recognize the Difference of Squares

When you see an algebraic expression in the form a² - b², where both a and b are perfect square numbers or expressions, you can apply the difference of squares formula.

Examples

Example 1: Factor the expression x² - 16

Using the difference of squares formula, we have:

x² - 16 = (x + 4)(x - 4)

Example 2: Factor the expression 9y² - 25

Using the difference of squares formula, we have:

9y² - 25 = (3y + 5)(3y - 5)

Practice Problems

1. Factor the following expressions using the difference of squares formula:

1. a² - 25
2. 4x² - 9
3. 16m² - 81n²

Summary

Understanding the difference of squares formula is important in algebra as it allows us to factor expressions and simplify calculations. By recognizing the pattern and applying the formula, we can efficiently factorize expressions and solve problems.