Question
Answer
$$(1+8u+24u^2+32u^3)^2=1024u^6+1536u^5+1088u^4+448u^3+112u^2+16u+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+8u+24u^2+32u^3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1024u^6+1536u^5+1088u^4+448u^3+112u^2+16u+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+8u+24u^2+32u^3}\right) $ by each term in $ \left( 1+8u+24u^2+32u^3\right) $. $$ \left( \color{blue}{1+8u+24u^2+32u^3}\right) \cdot \left( 1+8u+24u^2+32u^3\right) = \\ = 1+8u+24u^2+32u^3+8u+64u^2+192u^3+256u^4+24u^2+192u^3+576u^4+768u^5+32u^3+256u^4+768u^5+1024u^6 $$ |
| ② | Combine like terms: $$ 1+ \color{blue}{8u} + \color{red}{24u^2} + \color{green}{32u^3} + \color{blue}{8u} + \color{orange}{64u^2} + \color{blue}{192u^3} + \color{red}{256u^4} + \color{orange}{24u^2} + \color{green}{192u^3} + \color{orange}{576u^4} + \color{blue}{768u^5} + \color{green}{32u^3} + \color{orange}{256u^4} + \color{blue}{768u^5} +1024u^6 = \\ = 1024u^6+ \color{blue}{1536u^5} + \color{orange}{1088u^4} + \color{green}{448u^3} + \color{orange}{112u^2} + \color{blue}{16u} +1 $$ |
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