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Chapter 0: Problem 126

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

Short Answer

Expert verified
The factored form of \(x^2 - 9\) is \((x + 3)(x - 3)\).

Step by step solution

01

Identify the Squares

First, you need to identify the squares within the expression you want to factor. Suppose you have the expression \(x^2 - 9\). Here, \(x^2\) and \(9\) are your squares.
02

Find the Square Roots

Next, you find the square root of each of those squares. The square root of \(x^2\) is \(x\) and the square root of \(9\) is \(3\). So, your \(a\) and \(b\) are \(x\) and \(3\) respectively.
03

Apply the Difference of Squares Formula

Use the values of \(a\) and \(b\) and plug them into the difference of squares formula which is \((a+b)(a-b)\). If you put your \(a\) as \(x\) and \(b\) as \(3\) in the formula you get: \((x + 3)(x - 3)\).

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Most popular questions from this chapter

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(49 x^{-2} y^{4}\right)^{-\frac{1}{2}}\left(x y^{\frac{1}{2}}\right) $$

Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$

Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

What does it mean to factor completely?
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