Answer
$$(x^4+4x^3+16x^2+24x+52)(3x^2+16x+29)=3x^6+28x^5+141x^4+444x^3+1004x^2+1528x+1508$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^4+4x^3+16x^2+24x+52)(3x^2+16x+29)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^6+28x^5+141x^4+444x^3+1004x^2+1528x+1508\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^4+4x^3+16x^2+24x+52}\right) $ by each term in $ \left( 3x^2+16x+29\right) $. $$ \left( \color{blue}{x^4+4x^3+16x^2+24x+52}\right) \cdot \left( 3x^2+16x+29\right) = \\ = 3x^6+16x^5+29x^4+12x^5+64x^4+116x^3+48x^4+256x^3+464x^2+72x^3+384x^2+696x+156x^2+832x+1508 $$ |
| ② | Combine like terms: $$ 3x^6+ \color{blue}{16x^5} + \color{red}{29x^4} + \color{blue}{12x^5} + \color{green}{64x^4} + \color{orange}{116x^3} + \color{green}{48x^4} + \color{blue}{256x^3} + \color{red}{464x^2} + \color{blue}{72x^3} + \color{green}{384x^2} + \color{orange}{696x} + \color{green}{156x^2} + \color{orange}{832x} +1508 = \\ = 3x^6+ \color{blue}{28x^5} + \color{green}{141x^4} + \color{blue}{444x^3} + \color{green}{1004x^2} + \color{orange}{1528x} +1508 $$ |
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