Question
Multiply polynomial $ \, \color{blue}{ -5x^3+5x^2+7x } \, $ by $ \, \color{orangered}{ -3x+9 }$.
Answer
$$ \left( \color{blue}{-5x^3+5x^2+7x} \right) \cdot \left( \color{orangered}{-3x+9} \right) = 15x^4-60x^3+24x^2+63x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-5x^3} & \color{blue}{5x^2} & \color{blue}{7x} \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{9} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-5x^3} & \color{blue}{5x^2} & \color{blue}{7x} \\ \hline \color{blue}{-3x} & \color{orangered}{15x^4} & \color{orangered}{-15x^3} & \color{orangered}{-21x^2} \\ \hline \color{blue}{9} & \color{orangered}{-45x^3} & \color{orangered}{45x^2} & \color{orangered}{63x} \\ \hline \end{darray} $$Combine like terms:
$$ 15x^4-15x^3-45x^3-21x^2 + 45x^2 + 63x = \\ 15x^4-60x^3+24x^2+63x $$This page was created using
Polynomial Operations Calculator