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

$$ \left( \color{blue}{x^2-x+3} \right) \cdot \left( \color{orangered}{2x^2+4x-3} \right) = 2x^4+2x^3-x^2+15x-9 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{3} \\ \hline \color{blue}{2x^2} & \color{orangered}{2x^4} & \color{orangered}{-2x^3} & \color{orangered}{6x^2} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{-4x^2} & \color{orangered}{12x} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{3x} & \color{orangered}{-9} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^4-2x^3 + 4x^3 + 6x^2-4x^2-3x^2 + 12x + 3x-9 = \\ 2x^4+2x^3-x^2+15x-9 $$

Polynomial Operations Calculator