How to Factor the Difference of Two Perfect Squares
The difference of two perfect squares is a fundamental concept in algebra, often encountered in various mathematical problems. It is important to understand how to factor the difference of two perfect squares because it simplifies equations and aids in solving complex mathematical expressions. In this article, we will explore the process of factoring the difference of two perfect squares and provide you with a step-by-step guide to achieve this.
Firstly, let’s define what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. For example, 4, 9, 16, and 25 are all perfect squares because they can be written as 2^2, 3^2, 4^2, and 5^2, respectively.
Now, let’s consider the difference of two perfect squares, which can be represented as a^2 – b^2. To factor this expression, we can use the following formula:
a^2 – b^2 = (a + b)(a – b)
This formula is known as the difference of squares formula and is a crucial tool in factoring the difference of two perfect squares. The process involves identifying the square roots of the two perfect squares and then applying the formula.
Here’s a step-by-step guide on how to factor the difference of two perfect squares:
1. Identify the two perfect squares in the expression. For example, in the expression 16 – 9, the perfect squares are 16 and 9.
2. Find the square roots of the two perfect squares. In our example, the square roots are 4 and 3, respectively.
3. Apply the difference of squares formula: (a + b)(a – b). In our example, it becomes (4 + 3)(4 – 3).
4. Simplify the expression: (7)(1) = 7.
Therefore, the factored form of 16 – 9 is 7.
In conclusion, factoring the difference of two perfect squares is a straightforward process that involves identifying the perfect squares, finding their square roots, and applying the difference of squares formula. By following this guide, you will be able to factor the difference of two perfect squares with ease and confidence.
