Question
Multiply polynomial $ \, \color{blue}{ 3x^2-2x+3 } \, $ by $ \, \color{orangered}{ 4x^2+5x }$.
Answer
$$ \left( \color{blue}{3x^2-2x+3} \right) \cdot \left( \color{orangered}{4x^2+5x} \right) = 12x^4+7x^3+2x^2+15x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-2x} & \color{blue}{3} \\ \hline \color{blue}{4x^2} & & & \\ \hline \color{blue}{5x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-2x} & \color{blue}{3} \\ \hline \color{blue}{4x^2} & \color{orangered}{12x^4} & \color{orangered}{-8x^3} & \color{orangered}{12x^2} \\ \hline \color{blue}{5x} & \color{orangered}{15x^3} & \color{orangered}{-10x^2} & \color{orangered}{15x} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^4-8x^3 + 15x^3 + 12x^2-10x^2 + 15x = \\ 12x^4+7x^3+2x^2+15x $$This page was created using
Polynomial Operations Calculator