Answer
$$\frac{(-3x^3y)^6-(3x^{18}y^6+3x^6y^3+6x^6y^{18})}{3x^6y^3}=\frac{726x^{18}y^6-6x^6y^{18}-3x^6y^3}{3x^6y^3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(-3x^3y)^6-(3x^{18}y^6+3x^6y^3+6x^6y^{18})}{3x^6y^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{729x^{18}y^6-(3x^{18}y^6+3x^6y^3+6x^6y^{18})}{3x^6y^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{729x^{18}y^6-3x^{18}y^6-3x^6y^3-6x^6y^{18}}{3x^6y^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{726x^{18}y^6-6x^6y^{18}-3x^6y^3}{3x^6y^3}\end{aligned} $$ | |
| ① | $$ \left( -3x^3y \right)^6 = (-3)^6 \left( x^3 \right)^6y^6 = 729x^{18}y^6 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x^{18}y^6+3x^6y^3+6x^6y^{18} \right) = -3x^{18}y^6-3x^6y^3-6x^6y^{18} $$ |
| ③ | Simplify numerator $$ \color{blue}{729x^{18}y^6} \color{blue}{-3x^{18}y^6} -3x^6y^3-6x^6y^{18} = \color{blue}{726x^{18}y^6} -6x^6y^{18}-3x^6y^3 $$ |
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