Factor. \[ v^{2}-9 w^{2} \]

To factor the expression \( v^{2}-9 w^{2} \), we can recognize it as a difference of squares. The difference of squares can be expressed in the form \( a^{2} - b^{2} = (a - b)(a + b) \). Here, \( a = v \) and \( b = 3w \). So, we can rewrite the original expression as \( (v - 3w)(v + 3w) \). This shows that the expression is factored into two binomials: \( (v - 3w)(v + 3w) \). Let’s break it down: 1. Identify \( v^{2} \) as \( a^{2} \) and \( 9w^{2} \) as \( (3w)^{2} \). 2. Apply the difference of squares formula: \( a^{2} - b^{2} = (a - b)(a + b) \). 3. Conclude with \( (v - 3w)(v + 3w) \). So, \( v^{2}-9 w^{2} = (v - 3w)(v + 3w) \).