Question
Answer
$$(0.5+0.5x+0.5x^2+0.5x^3)^2=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(0.5+0.5x+0.5x^2+0.5x^3)^2& \xlongequal{ }(0.5+0x+0x^2+0x^3)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{00x0x^20x^3}\right) $ by each term in $ \left( 00x0x^20x^3\right) $. $$ \left( \color{blue}{00x0x^20x^3}\right) \cdot \left( 00x0x^20x^3\right) = \\ = 0 \cancel{0x} \cancel{0x^2} \cancel{0x^3} \cancel{0x} \cancel{0x^2} \cancel{0x^3} \cancel{0x^4} \cancel{0x^2} \cancel{0x^3} \cancel{0x^4} \cancel{0x^5} \cancel{0x^3} \cancel{0x^4} \cancel{0x^5}0x^6 $$ |
| ② | Combine like terms: $$ 0 \, \color{blue}{ \cancel{0x}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{blue}{ \cancel{0x}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^4}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^4}} \, \, \color{blue}{ \cancel{0x^5}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^4}} \, \, \color{blue}{ \cancel{0x^5}} \,0x^6 = 0 $$ |
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