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દ્વિપદી પ્રમેય

open parentheses straight x space minus fraction numerator 1 over denominator 2 straight x end fraction close parentheses to the power of 5 space comma space open parentheses x space not equal to space 0 close parentheses

વિસ્તરણ કરો :
$open parentheses straight x squared space plus space 1 over straight x close parentheses to the power of 5 space comma space open parentheses x space not equal to space 0 close parentheses$

open parentheses 1 space minus space 2 straight x close parentheses to the power of 4

અહીં, $straight a space equals space 1 comma space straight b space equals space minus 2 straight x space space અન ે space space straight n space equals space 4$

આ કિંમતો દ્વિપદી પ્રમેયમાં મૂકતાં,

$open parentheses 1 space minus space 2 straight x close parentheses to the power of 4 space equals space open parentheses table row cell table row 4 row 0 end table end cell end table close parentheses space open parentheses 1 close parentheses to the power of 4 space open parentheses negative 2 x close parentheses to the power of 0 space plus space open parentheses table row 4 row 1 end table close parentheses space open parentheses 1 close parentheses cubed space open parentheses negative 2 x close parentheses to the power of 1 space plus space open parentheses table row 4 row 2 end table close parentheses open parentheses 1 close parentheses squared open parentheses negative 2 x close parentheses squared space plus space open parentheses table row 4 row 3 end table close parentheses open parentheses 1 close parentheses to the power of 1 space open parentheses negative 2 x close parentheses cubed space plus space open parentheses table row 4 row 4 end table close parentheses space open parentheses 1 close parentheses to the power of 0 space open parentheses negative 2 x close parentheses to the power of 4 space space space space space space space space space space space space space space space space space space space equals space 1 space times space 1 space times space 1 space plus space 4 space times space 1 space times space open parentheses negative 2 x close parentheses space plus space 6 space times space open parentheses 4 x squared close parentheses space plus space 4 space times space 1 space times space open parentheses negative 8 x cubed close parentheses space plus space 1 space times space 1 space times space open parentheses 16 x to the power of 4 close parentheses space space space space space space space space space space space space space space space space space space space equals bold space bold 1 bold space bold minus bold space bold 8 bold italic x bold space bold plus bold space bold 24 bold space bold italic x to the power of bold 2 bold space bold minus bold space bold 32 bold italic x to the power of bold 3 bold space bold plus bold space bold 16 bold italic x to the power of bold 4$

open parentheses 3 straight x space minus space 2 close parentheses to the power of 6

વિસ્તરણ કરો :
$open parentheses 1 space plus space x space plus space x squared close parentheses to the power of 4$

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