Question
Multiply polynomial $ \, \color{blue}{ 2x-10 } \, $ by $ \, \color{orangered}{ x^2+7x+5 }$.
Answer
$$ \left( \color{blue}{2x-10} \right) \cdot \left( \color{orangered}{x^2+7x+5} \right) = 2x^3+4x^2-60x-50 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{7x} & \color{blue}{5} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-10} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{7x} & \color{blue}{5} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{14x^2} & \color{orangered}{10x} \\ \hline \color{blue}{-10} & \color{orangered}{-10x^2} & \color{orangered}{-70x} & \color{orangered}{-50} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 14x^2-10x^2 + 10x-70x-50 = \\ 2x^3+4x^2-60x-50 $$This page was created using
Polynomial Operations Calculator