Question
Answer
$$4xy(x+5y)-5x(2xy-2y^2)-3y(2x^2+5xy)=-12x^2y+15xy^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4xy(x+5y)-5x(2xy-2y^2)-3y(2x^2+5xy)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2y+20xy^2-(10x^2y-10xy^2)-(6x^2y+15xy^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2y+20xy^2-10x^2y+10xy^2-(6x^2y+15xy^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6x^2y+30xy^2-(6x^2y+15xy^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-6x^2y+30xy^2-6x^2y-15xy^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-12x^2y+15xy^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4xy} $ by $ \left( x+5y\right) $ $$ \color{blue}{4xy} \cdot \left( x+5y\right) = 4x^2y+20xy^2 $$Multiply $ \color{blue}{5x} $ by $ \left( 2xy-2y^2\right) $ $$ \color{blue}{5x} \cdot \left( 2xy-2y^2\right) = 10x^2y-10xy^2 $$Multiply $ \color{blue}{3y} $ by $ \left( 2x^2+5xy\right) $ $$ \color{blue}{3y} \cdot \left( 2x^2+5xy\right) = 6x^2y+15xy^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 10x^2y-10xy^2 \right) = -10x^2y+10xy^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{4x^2y} + \color{red}{20xy^2} \color{blue}{-10x^2y} + \color{red}{10xy^2} = \color{blue}{-6x^2y} + \color{red}{30xy^2} $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^2y+15xy^2 \right) = -6x^2y-15xy^2 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-6x^2y} + \color{red}{30xy^2} \color{blue}{-6x^2y} \color{red}{-15xy^2} = \color{blue}{-12x^2y} + \color{red}{15xy^2} $$ |
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