Question
Answer
$$(n+2)^2(n+1)=n^3+5n^2+8n+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n+2)^2(n+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1n^2+4n+4)(n+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}n^3+n^2+4n^2+4n+4n+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}n^3+5n^2+8n+4\end{aligned} $$ | |
| ① | Find $ \left(n+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ n } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(n+2\right)^2 = \color{blue}{n^2} +2 \cdot n \cdot 2 + \color{red}{2^2} = n^2+4n+4\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{n^2+4n+4}\right) $ by each term in $ \left( n+1\right) $. $$ \left( \color{blue}{n^2+4n+4}\right) \cdot \left( n+1\right) = n^3+n^2+4n^2+4n+4n+4 $$ |
| ③ | Combine like terms: $$ n^3+ \color{blue}{n^2} + \color{blue}{4n^2} + \color{red}{4n} + \color{red}{4n} +4 = n^3+ \color{blue}{5n^2} + \color{red}{8n} +4 $$ |
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