Factor completely, or state that the polynomial is prime. \( 81 x^{3}-24 y^{3} \) Select the correct choice below and fill in any answer boxes within your choice. A. \( 81 x^{3}-24 y^{3}=\square \) B. The polynomial is prime.

A. \( 81 x^{3}-24 y^{3}=(9x)^{3}-(2y)^{3}=(9x-2y)((9x)^{2}+(9x)(2y)+(2y)^{2})=(9x-2y)(81x^{2}+18xy+4y^{2}) \) Next time you encounter a difference of cubes, remember that it factors beautifully into the form \( a^3 - b^3 = (a-b)(a^2 + ab + b^2) \). It's like a magic trick that makes tough problems turn into manageable pieces! Want to impress your friends at a math gathering? Share that many polynomials seem prime at first glance, especially if they are of higher degrees or have unusual coefficients. Don't let the complexity fool you; with practice, you’ll start uncovering their hidden factors!