Multiply polynomial $ \, \color{blue}{ 4x-6 } \, $ by $ \, \color{orangered}{ x^2+3x+6 }$.

$$ \left( \color{blue}{4x-6} \right) \cdot \left( \color{orangered}{x^2+3x+6} \right) = 4x^3+6x^2+6x-36 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{3x} & \color{blue}{6} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{12x^2} & \color{orangered}{24x} \\ \hline \color{blue}{-6} & \color{orangered}{-6x^2} & \color{orangered}{-18x} & \color{orangered}{-36} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^3 + 12x^2-6x^2 + 24x-18x-36 = \\ 4x^3+6x^2+6x-36 $$

Polynomial Operations Calculator