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