Multiply polynomial $ \, \color{blue}{ 4x^2+12x-9 } \, $ by $ \, \color{orangered}{ x-3 }$.

$$ \left( \color{blue}{4x^2+12x-9} \right) \cdot \left( \color{orangered}{x-3} \right) = 4x^3-45x+27 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{12x} & \color{blue}{-9} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{12x} & \color{blue}{-9} \\ \hline \color{blue}{x} & \color{orangered}{4x^3} & \color{orangered}{12x^2} & \color{orangered}{-9x} \\ \hline \color{blue}{-3} & \color{orangered}{-12x^2} & \color{orangered}{-36x} & \color{orangered}{27} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^3 + 12x^2-12x^2-9x-36x + 27 = \\ 4x^3-45x+27 $$

Polynomial Operations Calculator