Question
Answer
$$(m^8+6m^4+1)^2=m^{16}+12m^{12}+38m^8+12m^4+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m^8+6m^4+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}m^{16}+12m^{12}+38m^8+12m^4+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{m^8+6m^4+1}\right) $ by each term in $ \left( m^8+6m^4+1\right) $. $$ \left( \color{blue}{m^8+6m^4+1}\right) \cdot \left( m^8+6m^4+1\right) = m^{16}+6m^{12}+m^8+6m^{12}+36m^8+6m^4+m^8+6m^4+1 $$ |
| ② | Combine like terms: $$ m^{16}+ \color{blue}{6m^{12}} + \color{red}{m^8} + \color{blue}{6m^{12}} + \color{green}{36m^8} + \color{orange}{6m^4} + \color{green}{m^8} + \color{orange}{6m^4} +1 = \\ = m^{16}+ \color{blue}{12m^{12}} + \color{green}{38m^8} + \color{orange}{12m^4} +1 $$ |
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