Answer
$$(x^3+8x^2+29x+52)(4x^3+12x^2+32x+52)=4x^6+44x^5+244x^4+864x^3+1968x^2+3172x+2704$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^3+8x^2+29x+52)(4x^3+12x^2+32x+52)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^6+44x^5+244x^4+864x^3+1968x^2+3172x+2704\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3+8x^2+29x+52}\right) $ by each term in $ \left( 4x^3+12x^2+32x+52\right) $. $$ \left( \color{blue}{x^3+8x^2+29x+52}\right) \cdot \left( 4x^3+12x^2+32x+52\right) = \\ = 4x^6+12x^5+32x^4+52x^3+32x^5+96x^4+256x^3+416x^2+116x^4+348x^3+928x^2+1508x+208x^3+624x^2+1664x+2704 $$ |
| ② | Combine like terms: $$ 4x^6+ \color{blue}{12x^5} + \color{red}{32x^4} + \color{green}{52x^3} + \color{blue}{32x^5} + \color{orange}{96x^4} + \color{blue}{256x^3} + \color{red}{416x^2} + \color{orange}{116x^4} + \color{green}{348x^3} + \color{orange}{928x^2} + \color{blue}{1508x} + \color{green}{208x^3} + \color{orange}{624x^2} + \color{blue}{1664x} +2704 = \\ = 4x^6+ \color{blue}{44x^5} + \color{orange}{244x^4} + \color{green}{864x^3} + \color{orange}{1968x^2} + \color{blue}{3172x} +2704 $$ |
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