Multiply polynomial $ \, \color{blue}{ x+7 } \, $ by $ \, \color{orangered}{ 8x^2-x-1 }$.

$$ \left( \color{blue}{x+7} \right) \cdot \left( \color{orangered}{8x^2-x-1} \right) = 8x^3+55x^2-8x-7 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^2} & \color{blue}{-x} & \color{blue}{-1} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{7} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^2} & \color{blue}{-x} & \color{blue}{-1} \\ \hline \color{blue}{x} & \color{orangered}{8x^3} & \color{orangered}{-x^2} & \color{orangered}{-x} \\ \hline \color{blue}{7} & \color{orangered}{56x^2} & \color{orangered}{-7x} & \color{orangered}{-7} \\ \hline \end{darray} $$

Combine like terms:

$$ 8x^3-x^2 + 56x^2-x-7x-7 = \\ 8x^3+55x^2-8x-7 $$

Polynomial Operations Calculator