Completely factor the expression by grouping, if possible.
\[
3 b^{2}-9+b^{2} y+3 y
\]

Step 1 ：Rearrange the terms in the expression \(3b^{2} - 9 + b^{2}y + 3y\) to \(3b^{2} + b^{2}y - 9 + 3y\).

Step 2 ：Group the terms as follows: \((3b^{2} + b^{2}y) + (-9 + 3y)\).

Step 3 ：Factor out the greatest common factor from each group. The common factor in the first two terms is \(b^{2}\), and the common factor in the last two terms is 3.

Step 4 ：The expression did not factor as expected. It seems that the expression cannot be factored by grouping.

Step 5 ：However, we can still factor out the common factors from each term. The common factor in the first two terms is \(b^{2}\), and the common factor in the last two terms is 3.

Step 6 ：Collect the terms to get \(b^{2}(y + 3) + 3*y - 9\).

Step 7 ：The completely factored expression by grouping is \(\boxed{b^{2}(y + 3) + 3(y - 3)}\).