Question
Answer
$$(x+1)(x+1)(x-2)=x^3-3x-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)(x+1)(x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x+x+1)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+2x+1)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-2x^2+2x^2-4x+x-2 \xlongequal{ } \\[1 em] & \xlongequal{ }x^3 -\cancel{2x^2}+ \cancel{2x^2}-4x+x-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-3x-2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x+1\right) = x^2+x+x+1 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} + \color{blue}{x} +1 = x^2+ \color{blue}{2x} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( x-2\right) = x^3 -\cancel{2x^2}+ \cancel{2x^2}-4x+x-2 $$ |
| ④ | Combine like terms: $$ x^3 \, \color{blue}{ -\cancel{2x^2}} \,+ \, \color{blue}{ \cancel{2x^2}} \, \color{green}{-4x} + \color{green}{x} -2 = x^3 \color{green}{-3x} -2 $$ |
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