Answer
$$k(2k-1)(2k+1)=4k^3-k$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}k(2k-1)(2k+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2k^2-k)(2k+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4k^3+2k^2-2k^2-k \xlongequal{ } \\[1 em] & \xlongequal{ }4k^3+ \cancel{2k^2} -\cancel{2k^2}-k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4k^3-k\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{k} $ by $ \left( 2k-1\right) $ $$ \color{blue}{k} \cdot \left( 2k-1\right) = 2k^2-k $$ |
| ② | Multiply each term of $ \left( \color{blue}{2k^2-k}\right) $ by each term in $ \left( 2k+1\right) $. $$ \left( \color{blue}{2k^2-k}\right) \cdot \left( 2k+1\right) = 4k^3+ \cancel{2k^2} -\cancel{2k^2}-k $$ |
| ③ | Combine like terms: $$ 4k^3+ \, \color{blue}{ \cancel{2k^2}} \, \, \color{blue}{ -\cancel{2k^2}} \,-k = 4k^3-k $$ |
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