Answer
$$(7n-1)^3-1=343n^3-147n^2+21n-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7n-1)^3-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}343n^3-147n^2+21n-1-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}343n^3-147n^2+21n-2\end{aligned} $$ | |
| 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: $$ 343n^3-147n^2+21n \color{blue}{-1} \color{blue}{-1} = 343n^3-147n^2+21n \color{blue}{-2} $$ |
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