Question

1. factor the difference of squares: ( x^2 - 64 )

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Identify \(a\) and \(b\) in the given expression

In the expression \(x^2-64\), we can rewrite \(64\) as \(8^2\). So, \(a = x\) and \(b = 8\) since \(x^2-64=x^2 - 8^2\).

Step3: Apply the difference of squares formula

Substituting \(a = x\) and \(b = 8\) into the formula \(a^2 - b^2=(a + b)(a - b)\), we get \((x + 8)(x - 8)\).

Answer:

\((x + 8)(x - 8)\)