\begin{tabular}{l} Question \\ Factor \( 2 x^{4}-50 x^{2} \) \\ None of these \\ 2x \( 2 x^{2}(x-5)^{2} \) \\ \( 2 x^{2}(x-5)(x+5) \) \\ \hline\end{tabular}

Did you know that the expression \(2x^{4}-50x^{2}\) can be factored neatly using the difference of squares? First, you can factor out \(2x^{2}\), giving you \(2x^{2}(x^{2}-25)\). Then, since \(x^{2}-25\) is a difference of squares, it can be further factored into \((x-5)(x+5)\). The final answer will be \(2x^{2}(x-5)(x+5)\), which is both a mathematical triumph and a practical tool for solving equations! When tackling factorization problems like this, a common mistake is forgetting to factor out the greatest common factor first. Always start by pulling out any common factors to simplify the expression as much as possible. This often reveals the structure of the polynomial and makes it easier to identify strategies like grouping or recognizing special forms such as quadratics or differences of squares!