Multiply polynomial $ \, \color{blue}{ 5x^2+8x+8 } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{5x^2+8x+8} \right) \cdot \left( \color{orangered}{2x+5} \right) = 10x^3+41x^2+56x+40 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{8x} & \color{blue}{8} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{8x} & \color{blue}{8} \\ \hline \color{blue}{2x} & \color{orangered}{10x^3} & \color{orangered}{16x^2} & \color{orangered}{16x} \\ \hline \color{blue}{5} & \color{orangered}{25x^2} & \color{orangered}{40x} & \color{orangered}{40} \\ \hline \end{darray} $$

Combine like terms:

$$ 10x^3 + 16x^2 + 25x^2 + 16x + 40x + 40 = \\ 10x^3+41x^2+56x+40 $$

Polynomial Operations Calculator