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Chapter 0: Problem 104

Explain how to factor the difference of two squares. Provide an example with your explanation.

Short Answer

Expert verified
The difference of squares \(a^2 - b^2\) can be factored using the formula \(a^2 - b^2 = (a - b)(a + b)\). An example of this is \(9x^2 - 25\) which factors to \((3x - 5)(3x + 5)\).

Step by step solution

01

Identifying a Difference of Squares

In algebra, a difference of squares is any expression of the form \(a^2 - b^2\). The first step in solving this problem will be identifying whether an algebraic expression fits this form.
02

Applying the Formula for Factoring

Once a difference of squares has been identified, one can use the formula for factoring a difference of squares. The formula states that \(a^2 - b^2 = (a - b)(a + b)\). This formula can be applied directly to simplify the algebraic expression.
03

Providing an Example

For example, consider the expression \(9x^2 - 25\). This is a difference of squares, with \(a^2 = 9x^2\) (and hence \(a = 3x\)) and \(b^2 = 25\) (and hence \(b = 5\)). Using the formula for factoring a difference of squares, the expression simplifies to \((3x - 5)(3x + 5)\).

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