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The expression \(16v^{2} - 9\) can be factored as \((4v - 3)(4v + 3)\).
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The Deep Dive
To factor the expression \( 16v^{2}-9 \), we can recognize that it is a difference of squares. This expression can be rewritten as \( (4v)^{2} - 3^{2} \). According to the difference of squares formula, which states that \( a^{2} - b^{2} = (a - b)(a + b) \), we can apply it here: \[ 16v^{2} - 9 = (4v - 3)(4v + 3) \] So, the factored form of the expression is \( (4v - 3)(4v + 3) \).
