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