Question
Answer
$$-2(2u-3)(3u+2)-12=-12u^2+10u$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(2u-3)(3u+2)-12& \xlongequal{ }-(4u-6)(3u+2)-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(12u^2+8u-18u-12)-12 \xlongequal{ } \\[1 em] & \xlongequal{ }-(12u^2-10u-12)-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-12u^2+10u+12-12 \xlongequal{ } \\[1 em] & \xlongequal{ }-12u^2+10u+ \cancel{12} -\cancel{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12u^2+10u\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4u-6}\right) $ by each term in $ \left( 3u+2\right) $. $$ \left( \color{blue}{4u-6}\right) \cdot \left( 3u+2\right) = 12u^2+8u-18u-12 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(12u^2-10u-12 \right) = -12u^2+10u+12 $$ |
| ③ | Combine like terms: $$ -12u^2+10u+ \, \color{blue}{ \cancel{12}} \, \, \color{blue}{ -\cancel{12}} \, = -12u^2+10u $$ |
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