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