Multiply polynomial $ \, \color{blue}{ 3x^2+5x-28 } \, $ by $ \, \color{orangered}{ 3x-7 }$.

$$ \left( \color{blue}{3x^2+5x-28} \right) \cdot \left( \color{orangered}{3x-7} \right) = 9x^3-6x^2-119x+196 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{5x} & \color{blue}{-28} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{5x} & \color{blue}{-28} \\ \hline \color{blue}{3x} & \color{orangered}{9x^3} & \color{orangered}{15x^2} & \color{orangered}{-84x} \\ \hline \color{blue}{-7} & \color{orangered}{-21x^2} & \color{orangered}{-35x} & \color{orangered}{196} \\ \hline \end{darray} $$

Combine like terms:

$$ 9x^3 + 15x^2-21x^2-84x-35x + 196 = \\ 9x^3-6x^2-119x+196 $$

Polynomial Operations Calculator