Question
Multiply polynomial $ \, \color{blue}{ x^2+6x } \, $ by $ \, \color{orangered}{ x^2-6x+4 }$.
Answer
$$ \left( \color{blue}{x^2+6x} \right) \cdot \left( \color{orangered}{x^2-6x+4} \right) = x^4-32x^2+24x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{6x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-6x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{6x} & \color{orangered}{6x^3} & \color{orangered}{-36x^2} & \color{orangered}{24x} \\ \hline \end{darray} $$Combine like terms:
$$ x^4-6x^3 + 6x^3 + 4x^2-36x^2 + 24x = \\ x^4-32x^2+24x $$This page was created using
Polynomial Operations Calculator