Question
Multiply polynomial $ \, \color{blue}{ q^2-2q+5 } \, $ by $ \, \color{orangered}{ q^2-5 }$.
Answer
$$ \left( \color{blue}{q^2-2q+5} \right) \cdot \left( \color{orangered}{q^2-5} \right) = q^4-2q^3+10q-25 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{q^2} & \color{blue}{-2q} & \color{blue}{5} \\ \hline \color{blue}{q^2} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{q^2} & \color{blue}{-2q} & \color{blue}{5} \\ \hline \color{blue}{q^2} & \color{orangered}{q^4} & \color{orangered}{-2q^3} & \color{orangered}{5q^2} \\ \hline \color{blue}{-5} & \color{orangered}{-5q^2} & \color{orangered}{10q} & \color{orangered}{-25} \\ \hline \end{darray} $$Combine like terms:
$$ q^4-2q^3-5q^2 + 5q^2 + 10q-25 = \\ q^4-2q^3+10q-25 $$This page was created using
Polynomial Operations Calculator