Question
Answer
$$(1+16x+72x^2+96x^3+24^4)^2=9216x^6+13824x^5+8256x^4+63703488x^3+47776144x^2+10616864x+110075977729$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+16x+72x^2+96x^3+24^4)^2& \xlongequal{ }(1+16x+72x^2+96x^3+331776)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(96x^3+72x^2+16x+331777)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9216x^6+13824x^5+8256x^4+63703488x^3+47776144x^2+10616864x+110075977729\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{1} +16x+72x^2+96x^3+ \color{blue}{331776} = 96x^3+72x^2+16x+ \color{blue}{331777} $$ |
| ② | Multiply each term of $ \left( \color{blue}{96x^3+72x^2+16x+331777}\right) $ by each term in $ \left( 96x^3+72x^2+16x+331777\right) $. $$ \left( \color{blue}{96x^3+72x^2+16x+331777}\right) \cdot \left( 96x^3+72x^2+16x+331777\right) = \\ = 9216x^6+6912x^5+1536x^4+31850592x^3+6912x^5+5184x^4+1152x^3+23887944x^2+1536x^4+1152x^3+256x^2+5308432x+31850592x^3+23887944x^2+5308432x+110075977729 $$ |
| ③ | Combine like terms: $$ 9216x^6+ \color{blue}{6912x^5} + \color{red}{1536x^4} + \color{green}{31850592x^3} + \color{blue}{6912x^5} + \color{orange}{5184x^4} + \color{blue}{1152x^3} + \color{red}{23887944x^2} + \color{orange}{1536x^4} + \color{green}{1152x^3} + \color{orange}{256x^2} + \color{blue}{5308432x} + \color{green}{31850592x^3} + \color{orange}{23887944x^2} + \color{blue}{5308432x} +110075977729 = \\ = 9216x^6+ \color{blue}{13824x^5} + \color{orange}{8256x^4} + \color{green}{63703488x^3} + \color{orange}{47776144x^2} + \color{blue}{10616864x} +110075977729 $$ |
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