Answer
$$(n^2+2n+2)(n^2+2n+1)=n^4+4n^3+7n^2+6n+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n^2+2n+2)(n^2+2n+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}n^4+4n^3+7n^2+6n+2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{n^2+2n+2}\right) $ by each term in $ \left( n^2+2n+1\right) $. $$ \left( \color{blue}{n^2+2n+2}\right) \cdot \left( n^2+2n+1\right) = n^4+2n^3+n^2+2n^3+4n^2+2n+2n^2+4n+2 $$ |
| ② | Combine like terms: $$ n^4+ \color{blue}{2n^3} + \color{red}{n^2} + \color{blue}{2n^3} + \color{green}{4n^2} + \color{orange}{2n} + \color{green}{2n^2} + \color{orange}{4n} +2 = n^4+ \color{blue}{4n^3} + \color{green}{7n^2} + \color{orange}{6n} +2 $$ |
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