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