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