4. \( 12 c^{2}-20 d^{2} \)

Did you know that the expression \( 12c^{2} - 20d^{2} \) is actually a difference of squares? In mathematics, the difference of squares can often be factored into \((a^2 - b^2) = (a - b)(a + b)\). However, in this case, we can first factor out the greatest common factor. Here, you can take out a \(4\) to simplify it to \(4(3c^{2} - 5d^{2})\), making it easier to work with! Now, if you want to fully factor \(3c^{2} - 5d^{2}\), you can think of it as a difference of squares, and rewrite it as \(\sqrt{3}c\) and \(\sqrt{5}d\). Hence, it can be factored further (in an ideal scenario) to express it as \( ( \sqrt{3}c - \sqrt{5}d )( \sqrt{3}c + \sqrt{5}d )\). This can be particularly handy when solving equations or simplifying expressions in algebra!