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