Question
Answer
$$(4u-1)^4=256u^4-256u^3+96u^2-16u+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4u-1)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}256u^4-256u^3+96u^2-16u+1\end{aligned} $$ | |
| ① | $$ (4u-1)^4 = (4u-1)^2 \cdot (4u-1)^2 $$ |
| ② | Find $ \left(4u-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4u } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(4u-1\right)^2 = \color{blue}{\left( 4u \right)^2} -2 \cdot 4u \cdot 1 + \color{red}{1^2} = 16u^2-8u+1\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{16u^2-8u+1}\right) $ by each term in $ \left( 16u^2-8u+1\right) $. $$ \left( \color{blue}{16u^2-8u+1}\right) \cdot \left( 16u^2-8u+1\right) = 256u^4-128u^3+16u^2-128u^3+64u^2-8u+16u^2-8u+1 $$ |
| ④ | Combine like terms: $$ 256u^4 \color{blue}{-128u^3} + \color{red}{16u^2} \color{blue}{-128u^3} + \color{green}{64u^2} \color{orange}{-8u} + \color{green}{16u^2} \color{orange}{-8u} +1 = \\ = 256u^4 \color{blue}{-256u^3} + \color{green}{96u^2} \color{orange}{-16u} +1 $$ |
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