Question
Answer
$$(n-4m)^4=256m^4-256m^3n+96m^2n^2-16mn^3+n^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n-4m)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}256m^4-256m^3n+96m^2n^2-16mn^3+n^4\end{aligned} $$ | |
| ① | $$ (n-4m)^4 = (n-4m)^2 \cdot (n-4m)^2 $$ |
| ② | Find $ \left(n-4m\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ n } $ and $ B = \color{red}{ 4m }$. $$ \begin{aligned}\left(n-4m\right)^2 = \color{blue}{n^2} -2 \cdot n \cdot 4m + \color{red}{\left( 4m \right)^2} = n^2-8mn+16m^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{n^2-8mn+16m^2}\right) $ by each term in $ \left( n^2-8mn+16m^2\right) $. $$ \left( \color{blue}{n^2-8mn+16m^2}\right) \cdot \left( n^2-8mn+16m^2\right) = \\ = n^4-8mn^3+16m^2n^2-8mn^3+64m^2n^2-128m^3n+16m^2n^2-128m^3n+256m^4 $$ |
| ④ | Combine like terms: $$ n^4 \color{blue}{-8mn^3} + \color{red}{16m^2n^2} \color{blue}{-8mn^3} + \color{green}{64m^2n^2} \color{orange}{-128m^3n} + \color{green}{16m^2n^2} \color{orange}{-128m^3n} +256m^4 = \\ = 256m^4 \color{orange}{-256m^3n} + \color{green}{96m^2n^2} \color{blue}{-16mn^3} +n^4 $$ |
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