Multiply polynomial $ \, \color{blue}{ 2x+4 } \, $ by $ \, \color{orangered}{ 5x^2-x+3 }$.

$$ \left( \color{blue}{2x+4} \right) \cdot \left( \color{orangered}{5x^2-x+3} \right) = 10x^3+18x^2+2x+12 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{3} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{3} \\ \hline \color{blue}{2x} & \color{orangered}{10x^3} & \color{orangered}{-2x^2} & \color{orangered}{6x} \\ \hline \color{blue}{4} & \color{orangered}{20x^2} & \color{orangered}{-4x} & \color{orangered}{12} \\ \hline \end{darray} $$

Combine like terms:

$$ 10x^3-2x^2 + 20x^2 + 6x-4x + 12 = \\ 10x^3+18x^2+2x+12 $$

Polynomial Operations Calculator