Multiply $ \dfrac{7}{3y^2+23y+14} $ by $ \dfrac{y}{3y^2+26y+16} $ to get $ \dfrac{7y}{9y^4+147y^3+688y^2+732y+224} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7}{3y^2+23y+14} \cdot \frac{y}{3y^2+26y+16} & \xlongequal{\text{Step 1}} \frac{ 7 \cdot y }{ \left( 3y^2+23y+14 \right) \cdot \left( 3y^2+26y+16 \right) } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 7y }{ 9y^4+78y^3+48y^2+69y^3+598y^2+368y+42y^2+364y+224 } = \frac{7y}{9y^4+147y^3+688y^2+732y+224} \end{aligned} $$