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