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