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