Answer
$$(x-3)^4=x^4-12x^3+54x^2-108x+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-3)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-12x^3+54x^2-108x+81\end{aligned} $$ | |
| ① | $$ (x-3)^4 = (x-3)^2 \cdot (x-3)^2 $$ |
| ② | Find $ \left(x-3\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}{ 3 }$. $$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-6x+9}\right) $ by each term in $ \left( x^2-6x+9\right) $. $$ \left( \color{blue}{x^2-6x+9}\right) \cdot \left( x^2-6x+9\right) = x^4-6x^3+9x^2-6x^3+36x^2-54x+9x^2-54x+81 $$ |
| ④ | Combine like terms: $$ x^4 \color{blue}{-6x^3} + \color{red}{9x^2} \color{blue}{-6x^3} + \color{green}{36x^2} \color{orange}{-54x} + \color{green}{9x^2} \color{orange}{-54x} +81 = \\ = x^4 \color{blue}{-12x^3} + \color{green}{54x^2} \color{orange}{-108x} +81 $$ |
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