Question
Multiply polynomial $ \, \color{blue}{ 30x^2+15x-20 } \, $ by $ \, \color{orangered}{ 10x+5 }$.
Answer
$$ \left( \color{blue}{30x^2+15x-20} \right) \cdot \left( \color{orangered}{10x+5} \right) = 300x^3+300x^2-125x-100 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{30x^2} & \color{blue}{15x} & \color{blue}{-20} \\ \hline \color{blue}{10x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{30x^2} & \color{blue}{15x} & \color{blue}{-20} \\ \hline \color{blue}{10x} & \color{orangered}{300x^3} & \color{orangered}{150x^2} & \color{orangered}{-200x} \\ \hline \color{blue}{5} & \color{orangered}{150x^2} & \color{orangered}{75x} & \color{orangered}{-100} \\ \hline \end{darray} $$Combine like terms:
$$ 300x^3 + 150x^2 + 150x^2-200x + 75x-100 = \\ 300x^3+300x^2-125x-100 $$This page was created using
Polynomial Operations Calculator