Answer
$$(-x^2+x)^3=-x^6+3x^5-3x^4+x^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x^2+x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3-3x^4+3x^5-x^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^6+3x^5-3x^4+x^3\end{aligned} $$ | |
| ① | Find $ \left(-x^2+x\right)^3 $ in two steps. S1: Swap two terms inside bracket S2: apply formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = x^2 $. $$ \left(-x^2+x\right)^3 \xlongequal{ S1 } \left(x-x^2\right)^3 = x^3-3 \cdot x^2 \cdot x^2 + 3 \cdot x \cdot \left( x^2 \right)^2-\left( x^2 \right)^3 = x^3-3x^4+3x^5-x^6 $$ |
| ② | Combine like terms: $$ -x^6+3x^5-3x^4+x^3 = -x^6+3x^5-3x^4+x^3 $$ |
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