Answer
$$(x^2+0.13x+1.08)(0.1x^2+0.03x+0.08)-(0.03x+0.08)(0.03x+0.08)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+0.13x+1.08)(0.1x^2+0.03x+0.08)-(0.03x+0.08)(0.03x+0.08)& \xlongequal{ }(x^2+0x+1.08)(0x^2+0x+0.08)-(0x+0.08)(0x+0.08) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0-(0x^2+0x+0x+0) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0-0 \xlongequal{ } \\[1 em] & \xlongequal{ }0\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^20x+1}\right) $ by each term in $ \left( 0x^20x0\right) $. $$ \left( \color{blue}{x^20x+1}\right) \cdot \left( 0x^20x0\right) = \\ = 0x^4 \cancel{0x^3} \cancel{0x^2} \cancel{0x^3} \cancel{0x^2} \cancel{0x} \cancel{0x^2} \cancel{0x}0 $$ |
| ② | Combine like terms: $$ 0x^4 \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \, \, \color{blue}{ \cancel{0x^2}} \, \, \color{green}{ \cancel{0x}} \,0 = 0 $$Multiply each term of $ \left( \color{blue}{0x0}\right) $ by each term in $ \left( 0x0\right) $. $$ \left( \color{blue}{0x0}\right) \cdot \left( 0x0\right) = 0x^2 \cancel{0x} \cancel{0x}0 $$ |
| ③ | Combine like terms: $$ 0x^2 \, \color{blue}{ \cancel{0x}} \, \, \color{blue}{ \cancel{0x}} \,0 = 0 $$ |
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