$${\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}^{{\mathtt{n}}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{nx}}}{{\mathtt{1}}{!}}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({n}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}{!}}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\sqrt{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{\frac{\left({\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}^{{\mathtt{n}}}{\mathtt{\,-\,}}{\mathtt{nx}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{n}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}}}}\right)\\
{\mathtt{x}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{\frac{\left({\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}^{{\mathtt{n}}}{\mathtt{\,-\,}}{\mathtt{nx}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{n}{\left({\mathtt{n}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}}}}\\
\end{array} \right\}$$ what is this used for?
+33615 The expression in the subject title of your question illustrates the first few terms of the binomial expansion (which has lots of uses in mathematics) - see https://en.wikipedia.org/wiki/Binomial_theorem for more information.
In the body of your question the solver has assumed you want to equate the left-hand side with the right-hand side and has assumed nx is a variable in its own right (it doesn't recognise implicit multiplication). Strangely, it has also assumed (1+x)n is also a single variable (!) and has solved the equation as if it were a quadratic.
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+33615 The expression in the subject title of your question illustrates the first few terms of the binomial expansion (which has lots of uses in mathematics) - see https://en.wikipedia.org/wiki/Binomial_theorem for more information.
In the body of your question the solver has assumed you want to equate the left-hand side with the right-hand side and has assumed nx is a variable in its own right (it doesn't recognise implicit multiplication). Strangely, it has also assumed (1+x)n is also a single variable (!) and has solved the equation as if it were a quadratic.
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