Question
Multiply polynomial $ \, \color{blue}{ b^2-8b+1 } \, $ by $ \, \color{orangered}{ b-7 }$.
Answer
$$ \left( \color{blue}{b^2-8b+1} \right) \cdot \left( \color{orangered}{b-7} \right) = b^3-15b^2+57b-7 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{b^2} & \color{blue}{-8b} & \color{blue}{1} \\ \hline \color{blue}{b} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{b^2} & \color{blue}{-8b} & \color{blue}{1} \\ \hline \color{blue}{b} & \color{orangered}{b^3} & \color{orangered}{-8b^2} & \color{orangered}{b} \\ \hline \color{blue}{-7} & \color{orangered}{-7b^2} & \color{orangered}{56b} & \color{orangered}{-7} \\ \hline \end{darray} $$Combine like terms:
$$ b^3-8b^2-7b^2 + b + 56b-7 = \\ b^3-15b^2+57b-7 $$This page was created using
Polynomial Operations Calculator