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

$$ \left( \color{blue}{x^2+4x+2} \right) \cdot \left( \color{orangered}{2x+2} \right) = 2x^3+10x^2+12x+4 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{2} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{8x^2} & \color{orangered}{4x} \\ \hline \color{blue}{2} & \color{orangered}{2x^2} & \color{orangered}{8x} & \color{orangered}{4} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^3 + 8x^2 + 2x^2 + 4x + 8x + 4 = \\ 2x^3+10x^2+12x+4 $$

Polynomial Operations Calculator