Find the product \( \frac{8}{6 n-4} \cdot\left(9 n^{2}-4\right) \) An expression can be written in rational form by writing it as a fraction with a denominator of

To simplify the product \( \frac{8}{6n-4} \cdot (9n^2 - 4) \), we first notice that \( 9n^2 - 4 \) can be factored as a difference of squares: \( (3n - 2)(3n + 2) \). Next, we can simplify the denominator \( 6n - 4 \) as follows: \( 6n - 4 = 2(3n - 2) \). Putting it all together, we have: \[ \frac{8}{2(3n-2)} \cdot (3n - 2)(3n + 2) = \frac{8(3n + 2)}{2} = 4(3n + 2) = 12n + 8. \] Now you have your simplified expression! On to our next bit of fun: knowing how to factor and simplify is like being a treasure hunter! Finding the right factors can uncover hidden gems in math. Don't forget that recognizing patterns, like the difference of squares and common factors, can save you tons of time and lead you to the solution treasure faster! Lastly, if you're ever stuck, try revisiting the basics. Many mistakes stem from jumping ahead without double-checking your foundations. Take a moment to analyze the problem step by step, and you'll likely catch any hiccups before they become bigger issues. Happy solving!