Question
Multiply polynomial $ \, \color{blue}{ 3w^3-5w^2+4 } \, $ by $ \, \color{orangered}{ 2w^4-5 }$.
Answer
$$ \left( \color{blue}{3w^3-5w^2+4} \right) \cdot \left( \color{orangered}{2w^4-5} \right) = 6w^7-10w^6+8w^4-15w^3+25w^2-20 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3w^3} & \color{blue}{-5w^2} & \color{blue}{4} \\ \hline \color{blue}{2w^4} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3w^3} & \color{blue}{-5w^2} & \color{blue}{4} \\ \hline \color{blue}{2w^4} & \color{orangered}{6w^7} & \color{orangered}{-10w^6} & \color{orangered}{8w^4} \\ \hline \color{blue}{-5} & \color{orangered}{-15w^3} & \color{orangered}{25w^2} & \color{orangered}{-20} \\ \hline \end{darray} $$Combine like terms:
$$ 6w^7-10w^6-15w^3 + 8w^4 + 25w^2-20 = \\ 6w^7-10w^6+8w^4-15w^3+25w^2-20 $$This page was created using
Polynomial Operations Calculator