complete the factoring of the polynomial. \[ 2 x^{3} y^{3}-6 x y^{2}=2 x y^{2}(\square) \]

To complete the factoring of the polynomial \( 2 x^{3} y^{3}-6 x y^{2} \), we notice that we can factor out \( 2xy^2 \). This leaves us with the expression \( x^2y - 3 \) inside the parentheses. Thus, the completed factored form is: \[ 2 x y^{2}(x^2 y - 3) \] Did you know that factoring polynomials like this is not just a math exercise, but is also used in various real-world applications, such as simplifying formulas in physics or engineering? For instance, in calculating forces or properties of materials, simplifying expressions can lead to clearer understanding of relationships between different variables! When factoring, remember to always look for the greatest common factor first! A common mistake is jumping in without checking if there’s a larger factor, which can make the subsequent steps more complicated. Always keep your eyes peeled for what can be factored out first to ease the process! Happy factoring!