Question
Answer
$$(m+n^3)^4=n^{12}+4mn^9+6m^2n^6+4m^3n^3+m^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m+n^3)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}n^{12}+4mn^9+6m^2n^6+4m^3n^3+m^4\end{aligned} $$ | |
| ① | $$ (m+n^3)^4 = (m+n^3)^2 \cdot (m+n^3)^2 $$ |
| ② | Find $ \left(m+n^3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ m } $ and $ B = \color{red}{ n^3 }$. $$ \begin{aligned}\left(m+n^3\right)^2 = \color{blue}{m^2} +2 \cdot m \cdot n^3 + \color{red}{\left( n^3 \right)^2} = m^2+2mn^3+n^6\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{m^2+2mn^3+n^6}\right) $ by each term in $ \left( m^2+2mn^3+n^6\right) $. $$ \left( \color{blue}{m^2+2mn^3+n^6}\right) \cdot \left( m^2+2mn^3+n^6\right) = \\ = m^4+2m^3n^3+m^2n^6+2m^3n^3+4m^2n^6+2mn^9+m^2n^6+2mn^9+n^{12} $$ |
| ④ | Combine like terms: $$ m^4+ \color{blue}{2m^3n^3} + \color{red}{m^2n^6} + \color{blue}{2m^3n^3} + \color{green}{4m^2n^6} + \color{orange}{2mn^9} + \color{green}{m^2n^6} + \color{orange}{2mn^9} +n^{12} = \\ = n^{12}+ \color{orange}{4mn^9} + \color{green}{6m^2n^6} + \color{blue}{4m^3n^3} +m^4 $$ |
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