Answer
$$(-3x+18)^3=-27x^3+486x^2-2916x+5832$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-3x+18)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5832-2916x+486x^2-27x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-27x^3+486x^2-2916x+5832\end{aligned} $$ | |
| ① | Find $ \left(-3x+18\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 = 18 $ and $ B = 3x $. $$ \left(-3x+18\right)^3 \xlongequal{ S1 } \left(18-3x\right)^3 = 18^3-3 \cdot 18^2 \cdot 3x + 3 \cdot 18 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 5832-2916x+486x^2-27x^3 $$ |
| ② | Combine like terms: $$ -27x^3+486x^2-2916x+5832 = -27x^3+486x^2-2916x+5832 $$ |
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