Question
Answer
$$(x-0.001)^4=x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-0.001)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4\end{aligned} $$ | |
| ① | $$ (x0)^4 = (x0)^2 \cdot (x0)^2 $$ |
| ② | Find $ \left(x+0\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}{ 0 }$. $$ \begin{aligned}\left(x+0\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 0 + \color{red}{0^2} = x^20x0\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^20x0}\right) $ by each term in $ \left( x^20x0\right) $. $$ \left( \color{blue}{x^20x0}\right) \cdot \left( x^20x0\right) = \\ = x^4 \cancel{0x^3} \cancel{0x^2} \cancel{0x^3} \cancel{0x^2} \cancel{0x} \cancel{0x^2} \cancel{0x}0 $$ |
| ④ | Combine like terms: $$ x^4 \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \,0 = x^4 $$ |
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