Multiply polynomial $ \, \color{blue}{ d^2-4d+4 } \, $ by $ \, \color{orangered}{ 3d+1 }$.

$$ \left( \color{blue}{d^2-4d+4} \right) \cdot \left( \color{orangered}{3d+1} \right) = 3d^3-11d^2+8d+4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{d^2} & \color{blue}{-4d} & \color{blue}{4} \\ \hline \color{blue}{3d} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{d^2} & \color{blue}{-4d} & \color{blue}{4} \\ \hline \color{blue}{3d} & \color{orangered}{3d^3} & \color{orangered}{-12d^2} & \color{orangered}{12d} \\ \hline \color{blue}{1} & \color{orangered}{d^2} & \color{orangered}{-4d} & \color{orangered}{4} \\ \hline \end{darray} $$

Combine like terms:

$$ 3d^3-12d^2 + d^2 + 12d-4d + 4 = \\ 3d^3-11d^2+8d+4 $$

Polynomial Operations Calculator