Problem 126
Question
Explain how to factor the difference of two squares. Provide an example with your explanation.
Step-by-Step Solution
Verified Answer
The factored form of \(x^2 - 9\) is \((x + 3)(x - 3)\).
1Step 1: 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.
2Step 2: 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.
3Step 3: 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: \((x + 3)(x - 3)\).
Other exercises in this chapter
Problem 126
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