Question
Multiply polynomial $ \, \color{blue}{ 2x^2-5x } \, $ by $ \, \color{orangered}{ 3x^2+9x+3 }$.
Answer
$$ \left( \color{blue}{2x^2-5x} \right) \cdot \left( \color{orangered}{3x^2+9x+3} \right) = 6x^4+3x^3-39x^2-15x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{9x} & \color{blue}{3} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-5x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{9x} & \color{blue}{3} \\ \hline \color{blue}{2x^2} & \color{orangered}{6x^4} & \color{orangered}{18x^3} & \color{orangered}{6x^2} \\ \hline \color{blue}{-5x} & \color{orangered}{-15x^3} & \color{orangered}{-45x^2} & \color{orangered}{-15x} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^4 + 18x^3-15x^3 + 6x^2-45x^2-15x = \\ 6x^4+3x^3-39x^2-15x $$This page was created using
Polynomial Operations Calculator