Answer
$$2(3y-4x)(x+2y)=-8x^2-10xy+12y^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(3y-4x)(x+2y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6y-8x)(x+2y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6xy+12y^2-8x^2-16xy \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-8x^2-10xy+12y^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 3y-4x\right) $ $$ \color{blue}{2} \cdot \left( 3y-4x\right) = 6y-8x $$ |
| ② | Multiply each term of $ \left( \color{blue}{6y-8x}\right) $ by each term in $ \left( x+2y\right) $. $$ \left( \color{blue}{6y-8x}\right) \cdot \left( x+2y\right) = 6xy+12y^2-8x^2-16xy $$ |
| ③ | Combine like terms: $$ \color{blue}{6xy} +12y^2-8x^2 \color{blue}{-16xy} = -8x^2 \color{blue}{-10xy} +12y^2 $$ |
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