Answer
$$(-x+3)^3=-x^3+9x^2-27x+27$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x+3)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}27-27x+9x^2-x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^3+9x^2-27x+27\end{aligned} $$ | |
| ① | Find $ \left(-x+3\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 = 3 $ and $ B = x $. $$ \left(-x+3\right)^3 \xlongequal{ S1 } \left(3-x\right)^3 = 3^3-3 \cdot 3^2 \cdot x + 3 \cdot 3 \cdot x^2-x^3 = 27-27x+9x^2-x^3 $$ |
| ② | Combine like terms: $$ -x^3+9x^2-27x+27 = -x^3+9x^2-27x+27 $$ |
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