Expand and simplify \( y(3 y+6)+3(3 y+4) \)

To expand and simplify the expression \( y(3y + 6) + 3(3y + 4) \), start by distributing the terms. First, expand \( y(3y + 6) \): \[ y(3y) + y(6) = 3y^2 + 6y \] Next, expand \( 3(3y + 4) \): \[ 3(3y) + 3(4) = 9y + 12 \] Now combine these expanded terms: \[ 3y^2 + 6y + 9y + 12 \] Combine like terms for \( y \): \[ 3y^2 + (6y + 9y) + 12 = 3y^2 + 15y + 12 \] Thus, the simplified expression is: \[ \boxed{3y^2 + 15y + 12} \]