Question
Multiply polynomial $ \, \color{blue}{ 2x^2-3 } \, $ by $ \, \color{orangered}{ x^2-3x+5 }$.
Answer
$$ \left( \color{blue}{2x^2-3} \right) \cdot \left( \color{orangered}{x^2-3x+5} \right) = 2x^4-6x^3+7x^2+9x-15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{5} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{5} \\ \hline \color{blue}{2x^2} & \color{orangered}{2x^4} & \color{orangered}{-6x^3} & \color{orangered}{10x^2} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{9x} & \color{orangered}{-15} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^4-6x^3-3x^2 + 10x^2 + 9x-15 = \\ 2x^4-6x^3+7x^2+9x-15 $$This page was created using
Polynomial Operations Calculator