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