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