Multiply polynomial $ \, \color{blue}{ 4x^2-x+6 } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{4x^2-x+6} \right) \cdot \left( \color{orangered}{2x+5} \right) = 8x^3+18x^2+7x+30 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-x} & \color{blue}{6} \\ \hline \color{blue}{2x} & \color{orangered}{8x^3} & \color{orangered}{-2x^2} & \color{orangered}{12x} \\ \hline \color{blue}{5} & \color{orangered}{20x^2} & \color{orangered}{-5x} & \color{orangered}{30} \\ \hline \end{darray} $$

Combine like terms:

$$ 8x^3-2x^2 + 20x^2 + 12x-5x + 30 = \\ 8x^3+18x^2+7x+30 $$

Polynomial Operations Calculator