Problem 39 - Algebra and Trigonometry

Question

Factor the difference of two squares. $$x^{2}-100$$

Step-by-Step Solution

Answer

The difference of squares is \(x^{2}-100 = (x-10)(x+10)\)

Step 1: Identify the terms

In this equation, \(x^{2}-100\), \(x^{2}\) is our first term (let's call it \(a^{2}\)) and \(100\) is the second term (let's call it \(b^{2}\)).

Step 2: Square root both terms

Take the square root of both \(a^{2}\) and \(b^{2}\). The square root of \(x^{2}\) is \(x\), so \(a=x\). The square root of \(100\) is \(10\), so \(b=10\).

Step 3: Use the Difference of squares

Now that we have our \(a\) and \(b\), we can substitute these values into the formula \(a^{2}-b^{2} = (a-b)(a+b)\). So, \(x^{2}-100 = (x-10)(x+10)\).