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