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