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