Question
Answer
$$(1+x+x^2)^3=x^6+3x^5+6x^4+7x^3+6x^2+3x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+x+x^2)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6+3x^5+6x^4+7x^3+6x^2+3x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+x+x^2}\right) $ by each term in $ \left( 1+x+x^2\right) $. $$ \left( \color{blue}{1+x+x^2}\right) \cdot \left( 1+x+x^2\right) = 1+x+x^2+x+x^2+x^3+x^2+x^3+x^4 $$ |
| ② | Combine like terms: $$ 1+ \color{blue}{x} + \color{red}{x^2} + \color{blue}{x} + \color{green}{x^2} + \color{orange}{x^3} + \color{green}{x^2} + \color{orange}{x^3} +x^4 = x^4+ \color{orange}{2x^3} + \color{green}{3x^2} + \color{blue}{2x} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4+2x^3+3x^2+2x+1}\right) $ by each term in $ \left( 1+x+x^2\right) $. $$ \left( \color{blue}{x^4+2x^3+3x^2+2x+1}\right) \cdot \left( 1+x+x^2\right) = \\ = x^4+x^5+x^6+2x^3+2x^4+2x^5+3x^2+3x^3+3x^4+2x+2x^2+2x^3+1+x+x^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{x^4} + \color{red}{x^5} +x^6+ \color{green}{2x^3} + \color{orange}{2x^4} + \color{red}{2x^5} + \color{blue}{3x^2} + \color{red}{3x^3} + \color{orange}{3x^4} + \color{green}{2x} + \color{orange}{2x^2} + \color{red}{2x^3} +1+ \color{green}{x} + \color{orange}{x^2} = \\ = x^6+ \color{red}{3x^5} + \color{orange}{6x^4} + \color{red}{7x^3} + \color{orange}{6x^2} + \color{green}{3x} +1 $$ |
This page was created using
Simplify polynomials calculator