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