Question
Multiply polynomial $ \, \color{blue}{ 5x^2-x-5 } \, $ by $ \, \color{orangered}{ 5x-3 }$.
Answer
$$ \left( \color{blue}{5x^2-x-5} \right) \cdot \left( \color{orangered}{5x-3} \right) = 25x^3-20x^2-22x+15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{-5} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{-5} \\ \hline \color{blue}{5x} & \color{orangered}{25x^3} & \color{orangered}{-5x^2} & \color{orangered}{-25x} \\ \hline \color{blue}{-3} & \color{orangered}{-15x^2} & \color{orangered}{3x} & \color{orangered}{15} \\ \hline \end{darray} $$Combine like terms:
$$ 25x^3-5x^2-15x^2-25x + 3x + 15 = \\ 25x^3-20x^2-22x+15 $$This page was created using
Polynomial Operations Calculator