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