Question
Answer
$$12k(k+1)^2=12k^3+24k^2+12k$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}12k(k+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}12k(1k^2+2k+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12k^3+24k^2+12k\end{aligned} $$ | |
| ① | Find $ \left(k+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}{ k } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(k+1\right)^2 = \color{blue}{k^2} +2 \cdot k \cdot 1 + \color{red}{1^2} = k^2+2k+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{12k} $ by $ \left( k^2+2k+1\right) $ $$ \color{blue}{12k} \cdot \left( k^2+2k+1\right) = 12k^3+24k^2+12k $$ |
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