Answer
$$(1-x)\cdot(2-x)\cdot(3-x)=-x^3+6x^2-11x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1-x)\cdot(2-x)\cdot(3-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2-x-2x+x^2)\cdot(3-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-3x+2)\cdot(3-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2-x^3-9x+3x^2+6-2x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-x^3+6x^2-11x+6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1-x}\right) $ by each term in $ \left( 2-x\right) $. $$ \left( \color{blue}{1-x}\right) \cdot \left( 2-x\right) = 2-x-2x+x^2 $$ |
| ② | Combine like terms: $$ 2 \color{blue}{-x} \color{blue}{-2x} +x^2 = x^2 \color{blue}{-3x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-3x+2}\right) $ by each term in $ \left( 3-x\right) $. $$ \left( \color{blue}{x^2-3x+2}\right) \cdot \left( 3-x\right) = 3x^2-x^3-9x+3x^2+6-2x $$ |
| ④ | Combine like terms: $$ \color{blue}{3x^2} -x^3 \color{red}{-9x} + \color{blue}{3x^2} +6 \color{red}{-2x} = -x^3+ \color{blue}{6x^2} \color{red}{-11x} +6 $$ |
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