Question
Answer
$$4n^3-n+3(2n+1)^2=4n^3+12n^2+11n+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4n^3-n+3(2n+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4n^3-n+3(4n^2+4n+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4n^3-n+12n^2+12n+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4n^3+12n^2+11n+3\end{aligned} $$ | |
| ① | Find $ \left(2n+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2n } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(2n+1\right)^2 = \color{blue}{\left( 2n \right)^2} +2 \cdot 2n \cdot 1 + \color{red}{1^2} = 4n^2+4n+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 4n^2+4n+1\right) $ $$ \color{blue}{3} \cdot \left( 4n^2+4n+1\right) = 12n^2+12n+3 $$ |
| ③ | Combine like terms: $$ 4n^3 \color{blue}{-n} +12n^2+ \color{blue}{12n} +3 = 4n^3+12n^2+ \color{blue}{11n} +3 $$ |
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