The Difference of Squares Formula: A Comprehensive Guide to Factoring Quadratic Expressions

Difference of Squares Formula

The difference of squares formula is a mathematical formula used to factorize a quadratic expression

The difference of squares formula is a mathematical formula used to factorize a quadratic expression. It is used when you have a quadratic expression in the form of a^2 – b^2.

The formula states that for any two numbers a and b, the expression a^2 – b^2 can be factored as (a + b)(a – b).

To understand this formula better, let’s break it down step by step:

1. Start with the quadratic expression a^2 – b^2.

2. Notice that this expression can also be written as (a)^2 – (b)^2.

3. Now, apply the formula for factoring a difference of squares: (a + b)(a – b).

4. Substitute a in place of a and b in place of b in the factored expression.

(a + b)(a – b)
(a + b) × (a – b)

5. You may observe that the expression you obtain after factoring is equivalent to the original quadratic expression.

Let’s take an example to see how this formula works:

Example: Factor the expression x^2 – 4.

In this example, a = x and b = 2.

Using the difference of squares formula, we can factorize x^2 – 4 as (x + 2)(x – 2).

When multiplying (x + 2) and (x – 2) together, we get x^2 – 4, which again matches the original quadratic expression.

The difference of squares formula is a useful tool for factoring quadratic expressions and can be used to simplify and solve various mathematical problems.

More Answers: