Multiply polynomial $ \, \color{blue}{ 9x^2+6x-8 } \, $ by $ \, \color{orangered}{ x+2 }$.

$$ \left( \color{blue}{9x^2+6x-8} \right) \cdot \left( \color{orangered}{x+2} \right) = 9x^3+24x^2+4x-16 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{6x} & \color{blue}{-8} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{6x} & \color{blue}{-8} \\ \hline \color{blue}{x} & \color{orangered}{9x^3} & \color{orangered}{6x^2} & \color{orangered}{-8x} \\ \hline \color{blue}{2} & \color{orangered}{18x^2} & \color{orangered}{12x} & \color{orangered}{-16} \\ \hline \end{darray} $$

Combine like terms:

$$ 9x^3 + 6x^2 + 18x^2-8x + 12x-16 = \\ 9x^3+24x^2+4x-16 $$

Polynomial Operations Calculator