Answer
$$(1+x+x^2)(1+8x+8x^2)=8x^4+16x^3+17x^2+9x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+x+x^2)(1+8x+8x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x^4+16x^3+17x^2+9x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+x+x^2}\right) $ by each term in $ \left( 1+8x+8x^2\right) $. $$ \left( \color{blue}{1+x+x^2}\right) \cdot \left( 1+8x+8x^2\right) = 1+8x+8x^2+x+8x^2+8x^3+x^2+8x^3+8x^4 $$ |
| ② | Combine like terms: $$ 1+ \color{blue}{8x} + \color{red}{8x^2} + \color{blue}{x} + \color{green}{8x^2} + \color{orange}{8x^3} + \color{green}{x^2} + \color{orange}{8x^3} +8x^4 = \\ = 8x^4+ \color{orange}{16x^3} + \color{green}{17x^2} + \color{blue}{9x} +1 $$ |
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