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