Multiply polynomial $ \, \color{blue}{ 9x+7 } \, $ by $ \, \color{orangered}{ 4x^2+x-4 }$.

$$ \left( \color{blue}{9x+7} \right) \cdot \left( \color{orangered}{4x^2+x-4} \right) = 36x^3+37x^2-29x-28 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{x} & \color{blue}{-4} \\ \hline \color{blue}{9x} & & & \\ \hline \color{blue}{7} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{x} & \color{blue}{-4} \\ \hline \color{blue}{9x} & \color{orangered}{36x^3} & \color{orangered}{9x^2} & \color{orangered}{-36x} \\ \hline \color{blue}{7} & \color{orangered}{28x^2} & \color{orangered}{7x} & \color{orangered}{-28} \\ \hline \end{darray} $$

Combine like terms:

$$ 36x^3 + 9x^2 + 28x^2-36x + 7x-28 = \\ 36x^3+37x^2-29x-28 $$

Polynomial Operations Calculator