1. Let's start by stating the problem: You want to understand how to factor expressions using the difference of squares method. 2. The difference of squares formula is: $$a^2 - b^2 = (a - b)(a + b)$$ This means that when you have one square term minus another square term, you can factor it into the product of two binomials. 3. Important rules: - Both terms must be perfect squares. - The operation between them must be subtraction (difference). 4. Example: Factor $$x^2 - 9$$. - Recognize that $$x^2$$ is a perfect square ($$x^2 = (x)^2$$). - Recognize that $$9$$ is a perfect square ($$9 = (3)^2$$). 5. Apply the formula: $$x^2 - 9 = (x - 3)(x + 3)$$ 6. Another example: Factor $$4y^2 - 25$$. - $$4y^2 = (2y)^2$$ and $$25 = 5^2$$. 7. Apply the formula: $$4y^2 - 25 = (2y - 5)(2y + 5)$$ 8. Summary: To use difference of squares, identify the squares and write the expression as the product of the sum and difference of their roots. This method helps simplify expressions and solve equations efficiently.