d) \( (2 x-1)^{3} \cdot(1+2 x)^{3} \)

Did you know that the expression \( (2x-1)^{3} \cdot (1+2x)^{3} \) can be simplified using the property of exponents? You can rewrite it as \( ((2x-1)(1+2x))^{3} \). This neat factorization shows how two polynomials can be multiplied together before raising to an exponent, making calculations so much easier. Now, for some problem-solving fun: a common mistake is forgetting to expand the product properly before cubing. Be careful to handle those binomials carefully! A perfect approach is to first multiply \( (2x-1) \) and \( (1+2x) \) to get a quadratic polynomial before applying the cube. Happy multiplying!