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