Answer
$$(7n+1)^3-1=343n^3+147n^2+21n$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7n+1)^3-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}343n^3+147n^2+21n+1-1 \xlongequal{ } \\[1 em] & \xlongequal{ }343n^3+147n^2+21n+ \cancel{1} -\cancel{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}343n^3+147n^2+21n\end{aligned} $$ | |
| ① | Find $ \left(7n+1\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 7n $ and $ B = 1 $. $$ \left(7n+1\right)^3 = \left( 7n \right)^3+3 \cdot \left( 7n \right)^2 \cdot 1 + 3 \cdot 7n \cdot 1^2+1^3 = 343n^3+147n^2+21n+1 $$ |
| ② | Combine like terms: $$ 343n^3+147n^2+21n+ \, \color{blue}{ \cancel{1}} \, \, \color{blue}{ -\cancel{1}} \, = 343n^3+147n^2+21n $$ |
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