Answer
$$(7n+2)^3-1=343n^3+294n^2+84n+7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7n+2)^3-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}343n^3+294n^2+84n+8-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}343n^3+294n^2+84n+7\end{aligned} $$ | |
| ① | Find $ \left(7n+2\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 7n $ and $ B = 2 $. $$ \left(7n+2\right)^3 = \left( 7n \right)^3+3 \cdot \left( 7n \right)^2 \cdot 2 + 3 \cdot 7n \cdot 2^2+2^3 = 343n^3+294n^2+84n+8 $$ |
| ② | Combine like terms: $$ 343n^3+294n^2+84n+ \color{blue}{8} \color{blue}{-1} = 343n^3+294n^2+84n+ \color{blue}{7} $$ |
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