Answer
$$(x-8)^4=x^4-32x^3+384x^2-2048x+4096$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-8)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-32x^3+384x^2-2048x+4096\end{aligned} $$ | |
| ① | $$ (x-8)^4 = (x-8)^2 \cdot (x-8)^2 $$ |
| ② | Find $ \left(x-8\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 8 }$. $$ \begin{aligned}\left(x-8\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 8 + \color{red}{8^2} = x^2-16x+64\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-16x+64}\right) $ by each term in $ \left( x^2-16x+64\right) $. $$ \left( \color{blue}{x^2-16x+64}\right) \cdot \left( x^2-16x+64\right) = \\ = x^4-16x^3+64x^2-16x^3+256x^2-1024x+64x^2-1024x+4096 $$ |
| ④ | Combine like terms: $$ x^4 \color{blue}{-16x^3} + \color{red}{64x^2} \color{blue}{-16x^3} + \color{green}{256x^2} \color{orange}{-1024x} + \color{green}{64x^2} \color{orange}{-1024x} +4096 = \\ = x^4 \color{blue}{-32x^3} + \color{green}{384x^2} \color{orange}{-2048x} +4096 $$ |
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