(A) -- savvasrealize com/dashboard/classes/669dd4d99101bf02dd0de829/c misncs (ICR) - 63415 or School: Additional Practico Factor out the greatest common factor from the folowing polynomial \[ 18 a^{3} b^{3}-18 a^{9} b^{2}+18 a b+27 a^{9} b \] Select the correct choice below and, it necessary, fill in the answer bax to complete your cho ce. A. \( 18 a^{3} b^{3}-18 a^{9} b^{9}+18 a b+27 a^{9} b= \) \( \square \) (Type your answer in lactored form.) B. The polynomial has no common factor other than 1 .

To factor out the greatest common factor from the polynomial \(18 a^{3} b^{3}-18 a^{9} b^{2}+18 a b+27 a^{9} b\), we first identify the coefficients and variable terms. The greatest common factor (GCF) of the coefficients (18, -18, 18, 27) is 9. For the variable parts, the maximum powers of \(a\) and \(b\) are \(a^{3}\) and \(b^{2}\), so the GCF is \(9a^{3}b^{2}\). Factoring this out, we rewrite the polynomial as: \[ 9a^{3}b^{2} \left( 2b - 2a^{6} + 2\frac{a}{b} + 3a^{6} \right) \] So, the answer is \( \boxed{9 a^{3} b^{2}(2 b - 2 a^{6} + 2 a/b + 3 a^{6})} \). The polynomial can be a wonderful way to explore deeper concepts in algebra while keeping our computations sharp and our thinking engaging. Factoring often serves as a gateway to simplifying and solving equations, leading you to appreciate how polynomials can reveal hidden relationships! In practice, recognizing how to factor will not only speed up your calculations but also enhance your understanding of variable relationships. When tackling polynomials, a common pitfall is overlooking the GCF; always double-check to not miss out on simplifying what seems complex at first glance!