Question
Answer
$$(1+2x+3x^2+4x^3)(1+2x+3x^2+4x^3)=16x^6+24x^5+25x^4+20x^3+10x^2+4x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+2x+3x^2+4x^3)(1+2x+3x^2+4x^3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16x^6+24x^5+25x^4+20x^3+10x^2+4x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+2x+3x^2+4x^3}\right) $ by each term in $ \left( 1+2x+3x^2+4x^3\right) $. $$ \left( \color{blue}{1+2x+3x^2+4x^3}\right) \cdot \left( 1+2x+3x^2+4x^3\right) = \\ = 1+2x+3x^2+4x^3+2x+4x^2+6x^3+8x^4+3x^2+6x^3+9x^4+12x^5+4x^3+8x^4+12x^5+16x^6 $$ |
| ② | Combine like terms: $$ 1+ \color{blue}{2x} + \color{red}{3x^2} + \color{green}{4x^3} + \color{blue}{2x} + \color{orange}{4x^2} + \color{blue}{6x^3} + \color{red}{8x^4} + \color{orange}{3x^2} + \color{green}{6x^3} + \color{orange}{9x^4} + \color{blue}{12x^5} + \color{green}{4x^3} + \color{orange}{8x^4} + \color{blue}{12x^5} +16x^6 = \\ = 16x^6+ \color{blue}{24x^5} + \color{orange}{25x^4} + \color{green}{20x^3} + \color{orange}{10x^2} + \color{blue}{4x} +1 $$ |
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