Question
Answer
$$(1+3x+x^2)(1+5x+4x^2)=4x^4+17x^3+20x^2+8x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+3x+x^2)(1+5x+4x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^4+17x^3+20x^2+8x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+3x+x^2}\right) $ by each term in $ \left( 1+5x+4x^2\right) $. $$ \left( \color{blue}{1+3x+x^2}\right) \cdot \left( 1+5x+4x^2\right) = 1+5x+4x^2+3x+15x^2+12x^3+x^2+5x^3+4x^4 $$ |
| ② | Combine like terms: $$ 1+ \color{blue}{5x} + \color{red}{4x^2} + \color{blue}{3x} + \color{green}{15x^2} + \color{orange}{12x^3} + \color{green}{x^2} + \color{orange}{5x^3} +4x^4 = \\ = 4x^4+ \color{orange}{17x^3} + \color{green}{20x^2} + \color{blue}{8x} +1 $$ |
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