What is the greatest common factor of \( \left(y^{2}-81\right) \) and \( (2 y+18) \) ? \( \begin{array}{llll}\text { A. }(y-9) & \text { B. }(y+9) & \text { C. } 2(y-9) & \text { D. } 2\end{array} \)

To find the greatest common factor of \( \left(y^{2}-81\right) \) and \( (2y+18) \), we need to factorize both expressions and then identify the common factors. 1. Factorize \( \left(y^{2}-81\right) \): \( y^{2}-81 \) is a difference of squares, which can be factored as \( (y+9)(y-9) \). 2. Factorize \( (2y+18) \): \( 2y+18 \) can be factored out by 2 as \( 2(y+9) \). Now, we can see that the common factor between \( (y+9)(y-9) \) and \( 2(y+9) \) is \( y+9 \). Therefore, the greatest common factor of \( \left(y^{2}-81\right) \) and \( (2y+18) \) is \( y+9 \), which corresponds to option B.