Answer
$$x(x^2+1)^2=x^5+2x^3+x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x^2+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x(x^4+2x^2+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^5+2x^3+x\end{aligned} $$ | |
| ① | Find $ \left(x^2+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x^2 } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(x^2+1\right)^2 = \color{blue}{\left( x^2 \right)^2} +2 \cdot x^2 \cdot 1 + \color{red}{1^2} = x^4+2x^2+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{x} $ by $ \left( x^4+2x^2+1\right) $ $$ \color{blue}{x} \cdot \left( x^4+2x^2+1\right) = x^5+2x^3+x $$ |
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