Multiply polynomial $ \, \color{blue}{ 6x^2+3x+1 } \, $ by $ \, \color{orangered}{ -19x^2-2 }$.

$$ \left( \color{blue}{6x^2+3x+1} \right) \cdot \left( \color{orangered}{-19x^2-2} \right) = -114x^4-57x^3-31x^2-6x-2 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{3x} & \color{blue}{1} \\ \hline \color{blue}{-19x^2} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{3x} & \color{blue}{1} \\ \hline \color{blue}{-19x^2} & \color{orangered}{-114x^4} & \color{orangered}{-57x^3} & \color{orangered}{-19x^2} \\ \hline \color{blue}{-2} & \color{orangered}{-12x^2} & \color{orangered}{-6x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ -114x^4-57x^3-12x^2-19x^2-6x-2 = \\ -114x^4-57x^3-31x^2-6x-2 $$

Polynomial Operations Calculator