Multiply polynomial $ \, \color{blue}{ s^2+3 } \, $ by $ \, \color{orangered}{ s^2+4s-2 }$.

$$ \left( \color{blue}{s^2+3} \right) \cdot \left( \color{orangered}{s^2+4s-2} \right) = s^4+4s^3+s^2+12s-6 $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{s^2} & \color{blue}{4s} & \color{blue}{-2} \\ \hline \color{blue}{s^2} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{s^2} & \color{blue}{4s} & \color{blue}{-2} \\ \hline \color{blue}{s^2} & \color{orangered}{s^4} & \color{orangered}{4s^3} & \color{orangered}{-2s^2} \\ \hline \color{blue}{3} & \color{orangered}{3s^2} & \color{orangered}{12s} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ s^4 + 4s^3 + 3s^2-2s^2 + 12s-6 = \\ s^4+4s^3+s^2+12s-6 $$

Polynomial Operations Calculator