Question
Multiply polynomial $ \, \color{blue}{ b^3+b^2 } \, $ by $ \, \color{orangered}{ b^2+7b+4 }$.
Answer
$$ \left( \color{blue}{b^3+b^2} \right) \cdot \left( \color{orangered}{b^2+7b+4} \right) = b^5+8b^4+11b^3+4b^2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{b^2} & \color{blue}{7b} & \color{blue}{4} \\ \hline \color{blue}{b^3} & & & \\ \hline \color{blue}{b^2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{b^2} & \color{blue}{7b} & \color{blue}{4} \\ \hline \color{blue}{b^3} & \color{orangered}{b^5} & \color{orangered}{7b^4} & \color{orangered}{4b^3} \\ \hline \color{blue}{b^2} & \color{orangered}{b^4} & \color{orangered}{7b^3} & \color{orangered}{4b^2} \\ \hline \end{darray} $$Combine like terms:
$$ b^5 + 7b^4 + b^4 + 4b^3 + 7b^3 + 4b^2 = \\ b^5+8b^4+11b^3+4b^2 $$This page was created using
Polynomial Operations Calculator