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