Question
Multiply polynomial $ \, \color{blue}{ 6x^3+2x } \, $ by $ \, \color{orangered}{ 8x^3-9x^2+5 }$.
Answer
$$ \left( \color{blue}{6x^3+2x} \right) \cdot \left( \color{orangered}{8x^3-9x^2+5} \right) = 48x^6-54x^5+16x^4+12x^3+10x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^3} & \color{blue}{-9x^2} & \color{blue}{5} \\ \hline \color{blue}{6x^3} & & & \\ \hline \color{blue}{2x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^3} & \color{blue}{-9x^2} & \color{blue}{5} \\ \hline \color{blue}{6x^3} & \color{orangered}{48x^6} & \color{orangered}{-54x^5} & \color{orangered}{30x^3} \\ \hline \color{blue}{2x} & \color{orangered}{16x^4} & \color{orangered}{-18x^3} & \color{orangered}{10x} \\ \hline \end{darray} $$Combine like terms:
$$ 48x^6-54x^5 + 16x^4 + 30x^3-18x^3 + 10x = \\ 48x^6-54x^5+16x^4+12x^3+10x $$This page was created using
Polynomial Operations Calculator