Question
Answer
$$(m+1)(m^2+1)(m^4-3m^2+1)=m^7+m^6-2m^5-2m^4-2m^3-2m^2+m+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m+1)(m^2+1)(m^4-3m^2+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1m^3+m+m^2+1)(m^4-3m^2+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}m^7+m^6-2m^5-2m^4-2m^3-2m^2+m+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{m+1}\right) $ by each term in $ \left( m^2+1\right) $. $$ \left( \color{blue}{m+1}\right) \cdot \left( m^2+1\right) = m^3+m+m^2+1 $$ |
| ② | Multiply each term of $ \left( \color{blue}{m^3+m+m^2+1}\right) $ by each term in $ \left( m^4-3m^2+1\right) $. $$ \left( \color{blue}{m^3+m+m^2+1}\right) \cdot \left( m^4-3m^2+1\right) = m^7-3m^5+m^3+m^5-3m^3+m+m^6-3m^4+m^2+m^4-3m^2+1 $$ |
| ③ | Combine like terms: $$ m^7 \color{blue}{-3m^5} + \color{red}{m^3} + \color{blue}{m^5} \color{red}{-3m^3} +m+m^6 \color{green}{-3m^4} + \color{orange}{m^2} + \color{green}{m^4} \color{orange}{-3m^2} +1 = \\ = m^7+m^6 \color{blue}{-2m^5} \color{green}{-2m^4} \color{red}{-2m^3} \color{orange}{-2m^2} +m+1 $$ |
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