Question
Answer
$$3(x^2+3y^2-8xy)-2(3x^2-4xy+6)=-3x^2-16xy+9y^2-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x^2+3y^2-8xy)-2(3x^2-4xy+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x^2+9y^2-24xy-(6x^2-8xy+12) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2+9y^2-24xy-6x^2+8xy-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3x^2-16xy+9y^2-12\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( x^2+3y^2-8xy\right) $ $$ \color{blue}{3} \cdot \left( x^2+3y^2-8xy\right) = 3x^2+9y^2-24xy $$Multiply $ \color{blue}{2} $ by $ \left( 3x^2-4xy+6\right) $ $$ \color{blue}{2} \cdot \left( 3x^2-4xy+6\right) = 6x^2-8xy+12 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^2-8xy+12 \right) = -6x^2+8xy-12 $$ |
| ③ | Combine like terms: $$ \color{blue}{3x^2} +9y^2 \color{red}{-24xy} \color{blue}{-6x^2} + \color{red}{8xy} -12 = \color{blue}{-3x^2} \color{red}{-16xy} +9y^2-12 $$ |
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