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