Question

1. $64u^2 - v^2$

Explanation:

Step1: Identify the formula

The expression \(64u^{2}-v^{2}\) is a difference of squares, which follows the formula \(a^{2}-b^{2}=(a + b)(a - b)\).

Step2: Rewrite the terms as squares

We can rewrite \(64u^{2}\) as \((8u)^{2}\) and \(v^{2}\) remains as \(v^{2}\). So now the expression is \((8u)^{2}-v^{2}\).

Step3: Apply the difference of squares formula

Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\) where \(a = 8u\) and \(b=v\), we get \((8u + v)(8u - v)\).

Answer:

\((8u + v)(8u - v)\)