Question
Answer
$$-y(2y+4x)(y-x)=4x^2y-2xy^2-2y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-y(2y+4x)(y-x)& \xlongequal{ }-(2y^2+4xy)(y-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(2y^3-2xy^2+4xy^2-4x^2y) \xlongequal{ } \\[1 em] & \xlongequal{ }-(-4x^2y+2xy^2+2y^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2y-2xy^2-2y^3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2y^2+4xy}\right) $ by each term in $ \left( y-x\right) $. $$ \left( \color{blue}{2y^2+4xy}\right) \cdot \left( y-x\right) = 2y^3-2xy^2+4xy^2-4x^2y $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(-4x^2y+2xy^2+2y^3 \right) = 4x^2y-2xy^2-2y^3 $$ |
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