Question
Multiply polynomial $ \, \color{blue}{ 9x-5 } \, $ by $ \, \color{orangered}{ 2x^2+12x-3 }$.
Answer
$$ \left( \color{blue}{9x-5} \right) \cdot \left( \color{orangered}{2x^2+12x-3} \right) = 18x^3+98x^2-87x+15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{12x} & \color{blue}{-3} \\ \hline \color{blue}{9x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{12x} & \color{blue}{-3} \\ \hline \color{blue}{9x} & \color{orangered}{18x^3} & \color{orangered}{108x^2} & \color{orangered}{-27x} \\ \hline \color{blue}{-5} & \color{orangered}{-10x^2} & \color{orangered}{-60x} & \color{orangered}{15} \\ \hline \end{darray} $$Combine like terms:
$$ 18x^3 + 108x^2-10x^2-27x-60x + 15 = \\ 18x^3+98x^2-87x+15 $$This page was created using
Polynomial Operations Calculator