Factor the following binomial. \[ 16-81 x^{2} \] \( ([?]+\square x)(\square-\square x) \)

To factor the binomial \( 16 - 81x^2 \), we can recognize it as a difference of squares. We rewrite it as \( (4)^2 - (9x)^2 \). Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we get: \[ (4 - 9x)(4 + 9x) \] So, the final factored form is \( (4 - 9x)(4 + 9x) \). Now, let’s spice things up with some extra fun facts! Think of how the difference of squares is like a math magician! It can transform the seemingly un-factorable into something neat and tidy. Anytime you see \( a^2 - b^2 \) lurking around, you know you have a magical moment waiting to happen. And, just like in life, when faced with a tough problem, always check if there’s a simpler way to break it down! Many math troubles can be solved by recognizing patterns like this one. Keep a keen eye out for squares and try turning complex expressions into manageable pieces!