Question
Answer
$$(m-2n)^4=m^4-8m^3n+24m^2n^2-32mn^3+16n^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m-2n)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}m^4-8m^3n+24m^2n^2-32mn^3+16n^4\end{aligned} $$ | |
| ① | $$ (m-2n)^4 = (m-2n)^2 \cdot (m-2n)^2 $$ |
| ② | Find $ \left(m-2n\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}{ 2n }$. $$ \begin{aligned}\left(m-2n\right)^2 = \color{blue}{m^2} -2 \cdot m \cdot 2n + \color{red}{\left( 2n \right)^2} = m^2-4mn+4n^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{m^2-4mn+4n^2}\right) $ by each term in $ \left( m^2-4mn+4n^2\right) $. $$ \left( \color{blue}{m^2-4mn+4n^2}\right) \cdot \left( m^2-4mn+4n^2\right) = \\ = m^4-4m^3n+4m^2n^2-4m^3n+16m^2n^2-16mn^3+4m^2n^2-16mn^3+16n^4 $$ |
| ④ | Combine like terms: $$ m^4 \color{blue}{-4m^3n} + \color{red}{4m^2n^2} \color{blue}{-4m^3n} + \color{green}{16m^2n^2} \color{orange}{-16mn^3} + \color{green}{4m^2n^2} \color{orange}{-16mn^3} +16n^4 = \\ = m^4 \color{blue}{-8m^3n} + \color{green}{24m^2n^2} \color{orange}{-32mn^3} +16n^4 $$ |
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