Questions: Use the special factoring methods to factor the following binomial. If it cannot be factored, indicate "Not Factorable". x^2 - 100

Solution Steps

To factor the given binomial \(x^2 - 100\), we can use the difference of squares method. The difference of squares formula is \(a^2 - b^2 = (a - b)(a + b)\). Here, \(x^2\) is \(a^2\) and \(100\) is \(b^2\), where \(b = 10\). Therefore, the expression can be factored as \((x - 10)(x + 10)\).

We start with the binomial expression \(x^2 - 100\).

The expression can be recognized as a difference of squares, where \(a^2 = x^2\) and \(b^2 = 100\). Here, \(b\) can be expressed as \(b = 10\) since \(10^2 = 100\).

Using the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\), we can factor the expression: \[ x^2 - 100 = (x - 10)(x + 10) \]

Final Answer