Answer
$$(x^2+1)(2x^4+3x+1)+(4x^3+2)(4x^2+4)=2x^6+16x^5+2x^4+19x^3+9x^2+3x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+1)(2x^4+3x+1)+(4x^3+2)(4x^2+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x^6+3x^3+x^2+2x^4+3x+1+16x^5+16x^3+8x^2+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^6+16x^5+2x^4+19x^3+9x^2+3x+9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+1}\right) $ by each term in $ \left( 2x^4+3x+1\right) $. $$ \left( \color{blue}{x^2+1}\right) \cdot \left( 2x^4+3x+1\right) = 2x^6+3x^3+x^2+2x^4+3x+1 $$Multiply each term of $ \left( \color{blue}{4x^3+2}\right) $ by each term in $ \left( 4x^2+4\right) $. $$ \left( \color{blue}{4x^3+2}\right) \cdot \left( 4x^2+4\right) = 16x^5+16x^3+8x^2+8 $$ |
| ② | Combine like terms: $$ 2x^6+ \color{blue}{3x^3} + \color{red}{x^2} +2x^4+3x+ \color{green}{1} +16x^5+ \color{blue}{16x^3} + \color{red}{8x^2} + \color{green}{8} = \\ = 2x^6+16x^5+2x^4+ \color{blue}{19x^3} + \color{red}{9x^2} +3x+ \color{green}{9} $$ |
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