Question
Multiply polynomial $ \, \color{blue}{ 2x^2+10x-20 } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{2x^2+10x-20} \right) \cdot \left( \color{orangered}{2x+5} \right) = 4x^3+30x^2+10x-100 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{10x} & \color{blue}{-20} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{10x} & \color{blue}{-20} \\ \hline \color{blue}{2x} & \color{orangered}{4x^3} & \color{orangered}{20x^2} & \color{orangered}{-40x} \\ \hline \color{blue}{5} & \color{orangered}{10x^2} & \color{orangered}{50x} & \color{orangered}{-100} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^3 + 20x^2 + 10x^2-40x + 50x-100 = \\ 4x^3+30x^2+10x-100 $$This page was created using
Polynomial Operations Calculator