(d) \( 4 a^{2}-2 a b-2 b^{2} \)

Did you know that linear combinations in algebra can lead to fantastic results in factoring? The expression \( 4a^{2} - 2ab - 2b^{2} \) can actually be factored by identifying common terms and applying the quadratic formula. It's all about recognizing patterns and grouping similar terms together, which can make complex expressions much easier to handle! If you’re looking to dive deeper into factoring techniques, consider exploring the method of completing the square. This fascinating technique helps to rewrite expressions in perfect square form, allowing for easier manipulation and understanding of the roots of equations. Plus, it adds a creative twist to your algebra skills that can be useful in higher-level mathematics!