Which expression is not equivalent to \( 36 x^{6}-25 y^{4} \) ? \( \begin{array}{ll}\text { (1) } 6^{2}\left(x^{3}\right)^{2}-5^{2}\left(y^{2}\right)^{2} & \text { (3) }\left(6 x^{6}-5 y^{4}\right)\left(6 x^{6}+5 y^{4}\right) \\ \text { (2) }\left(6 x^{3}-5 y^{2}\right)\left(6 x^{3}+5 y^{2}\right) & \text { (4) }\left(3 \cdot 2 x^{3}-5 y^{2}\right)\left(3 \cdot 2 x^{3}+5 y^{2}\right)\end{array} \)

To determine which expression is not equivalent to \( 36 x^{6}-25 y^{4} \), we can start by recognizing that this expression takes the form \( a^2 - b^2 \), which factors into \( (a-b)(a+b) \). Here, \( a = 6x^3 \) and \( b = 5y^2 \). The correct factoring gives us \( (6x^3 - 5y^2)(6x^3 + 5y^2) \), which corresponds to option (2). Options (1) and (4) are valid representations of the original expression, while option (3), \( (6 x^6 - 5 y^4)(6 x^6 + 5 y^4) \), mistakenly suggests factoring based on \( 36 x^{6}-25 y^{4} \) incorrectly as it doesn't align with our original \( a^2 - b^2 \) setup. Thus, option (3) is the one that is not equivalent. Here’s a little history nugget: the difference of squares, like \( a^2 - b^2 \), dates back to ancient Greek mathematicians! They laid the foundational work that led to our modern algebraic identities. And for a practical tip, always double-check your factorizations! A common mistake is to forget that each term’s coefficients and variables affect the overall expression. When simplifying or factoring, keep an eye out for signs and terms to avoid unintended errors.