Answer
$$0.5x(x+1)(x+1)(x+2)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}0.5x(x+1)(x+1)(x+2)& \xlongequal{ }0x(x+1)(x+1)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(0x^2+0x)(x+1)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(0x^3+0x^2+0x^2+0x)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}0x+0 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}0\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{0x} $ by $ \left( x+1\right) $ $$ \color{blue}{0x} \cdot \left( x+1\right) = 0x^20x $$ |
| ② | Multiply each term of $ \left( \color{blue}{0x^20x}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{0x^20x}\right) \cdot \left( x+1\right) = 0x^3 \cancel{0x^2} \cancel{0x^2}0x $$ |
| ③ | Combine like terms: $$ 0x^3 \, \color{blue}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^2}} \,0x = 0 $$ |
| ④ | Multiply $ \color{blue}{0} $ by $ \left( x+2\right) $ $$ \color{blue}{0} \cdot \left( x+2\right) = 0x0 $$ |
| ⑤ | Combine like terms: $$ 0 = 0 $$ |
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