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