Answer
$$6(36-4u)^2+4\cdot(36-4u)=96u^2-1744u+7920$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6(36-4u)^2+4\cdot(36-4u)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6(1296-288u+16u^2)+4\cdot(36-4u) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7776-1728u+96u^2+144-16u \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}96u^2-1744u+7920\end{aligned} $$ | |
| ① | Find $ \left(36-4u\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 36 } $ and $ B = \color{red}{ 4u }$. $$ \begin{aligned}\left(36-4u\right)^2 = \color{blue}{36^2} -2 \cdot 36 \cdot 4u + \color{red}{\left( 4u \right)^2} = 1296-288u+16u^2\end{aligned} $$ |
| ② | Multiply $ \color{blue}{6} $ by $ \left( 1296-288u+16u^2\right) $ $$ \color{blue}{6} \cdot \left( 1296-288u+16u^2\right) = 7776-1728u+96u^2 $$Multiply $ \color{blue}{4} $ by $ \left( 36-4u\right) $ $$ \color{blue}{4} \cdot \left( 36-4u\right) = 144-16u $$ |
| ③ | Combine like terms: $$ \color{blue}{7776} \color{red}{-1728u} +96u^2+ \color{blue}{144} \color{red}{-16u} = 96u^2 \color{red}{-1744u} + \color{blue}{7920} $$ |
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