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