Answer
$$(x^4+2x^2+5)^2-x^2=x^8+4x^6+14x^4+19x^2+25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^4+2x^2+5)^2-x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^8+4x^6+14x^4+20x^2+25-x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^8+4x^6+14x^4+19x^2+25\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^4+2x^2+5}\right) $ by each term in $ \left( x^4+2x^2+5\right) $. $$ \left( \color{blue}{x^4+2x^2+5}\right) \cdot \left( x^4+2x^2+5\right) = x^8+2x^6+5x^4+2x^6+4x^4+10x^2+5x^4+10x^2+25 $$ |
| ② | Combine like terms: $$ x^8+ \color{blue}{2x^6} + \color{red}{5x^4} + \color{blue}{2x^6} + \color{green}{4x^4} + \color{orange}{10x^2} + \color{green}{5x^4} + \color{orange}{10x^2} +25 = \\ = x^8+ \color{blue}{4x^6} + \color{green}{14x^4} + \color{orange}{20x^2} +25 $$ |
| ③ | Combine like terms: $$ x^8+4x^6+14x^4+ \color{blue}{20x^2} +25 \color{blue}{-x^2} = x^8+4x^6+14x^4+ \color{blue}{19x^2} +25 $$ |
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