Question
Answer
$$(x-1)(x-2)(x-1)=x^3-4x^2+5x-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x-2)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-2x-x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-3x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-x^2-3x^2+3x+2x-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-4x^2+5x-2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x-2\right) = x^2-2x-x+2 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-2x} \color{blue}{-x} +2 = x^2 \color{blue}{-3x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-3x+2}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^2-3x+2}\right) \cdot \left( x-1\right) = x^3-x^2-3x^2+3x+2x-2 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-x^2} \color{blue}{-3x^2} + \color{red}{3x} + \color{red}{2x} -2 = x^3 \color{blue}{-4x^2} + \color{red}{5x} -2 $$ |
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