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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


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


અહીં, straight a space equals space straight x squared comma space space straight b space equals space 1 over straight x space અન ે space straight n space equals space 5

આ કિંમતો દ્વિપદી પ્રમેયમાં મૂકતાં,

open parentheses straight x squared space plus space 1 over straight x close parentheses to the power of 5

equals space open parentheses table row 5 row 0 end table close parentheses space open parentheses x squared close parentheses to the power of 5 space open parentheses 1 over x close parentheses to the power of 0 space plus space open parentheses table row 5 row 1 end table close parentheses space open parentheses x squared close parentheses to the power of 4 space open parentheses 1 over x close parentheses to the power of 1 space plus space open parentheses table row 5 row 2 end table close parentheses space open parentheses x squared close parentheses cubed space open parentheses 1 over x close parentheses squared space plus space open parentheses table row 5 row 3 end table close parentheses space open parentheses x squared close parentheses squared space open parentheses 1 over x close parentheses cubed space plus space open parentheses table row 5 row 4 end table close parentheses open parentheses x squared close parentheses to the power of 1 space open parentheses 1 over x close parentheses to the power of 4 space plus space open parentheses table row 5 row 5 end table close parentheses space open parentheses x squared close parentheses to the power of 0 space open parentheses 1 over x close parentheses to the power of 5

equals space 1 times space x to the power of 10 times space 1 space plus space 5 space times space x to the power of 8 space times space 1 over x space plus space 10 space times space x to the power of 6 space end exponent times space 1 over x squared space plus space 10 space times space x to the power of 4 space times space space fraction numerator 1 over denominator x cubed space end fraction space plus space 5 space times space space x squared space space times space 1 over x to the power of 4 space plus space 1 space times space 1 space times space 1 over x to the power of 5

equals space bold italic x to the power of bold 10 bold space bold plus bold space bold 5 bold italic x to the power of bold 7 bold space bold plus bold space bold 10 bold space bold italic x to the power of bold 4 bold space bold plus bold space bold 10 bold italic x bold space bold plus bold space fraction numerator bold 5 over denominator bold x to the power of bold 2 bold space end fraction bold space bold plus bold space bold 1 over bold x to the power of bold 5


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

અહીં, straight a space equals space straight x comma space straight b space equals space minus fraction numerator 1 over denominator 2 straight x end fraction space અન ે space straight n space equals space 5

આ કિંમતો દ્વિપદી પ્રમેયમાં મૂકતાં,

open parentheses straight x space minus space fraction numerator 1 over denominator 2 straight x end fraction close parentheses to the power of 5 space equals space open parentheses table row 5 row 0 end table close parentheses open parentheses x close parentheses to the power of 5 open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses to the power of 0 space plus space open parentheses table row 5 row 1 end table close parentheses open parentheses x close parentheses to the power of 4 open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses to the power of 1 space plus space open parentheses table row 5 row 2 end table close parentheses open parentheses x close parentheses cubed open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses squared space plus space open parentheses table row 5 row 3 end table close parentheses open parentheses x close parentheses squared open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses cubed

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus space open parentheses table row 5 row 4 end table close parentheses open parentheses x close parentheses to the power of 1 open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses to the power of 4 space plus space open parentheses table row 5 row 5 end table close parentheses open parentheses x close parentheses to the power of 0 open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses to the power of 5


space space space space 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 x to the power of 5 space times space 1 space plus space 5 space times space x to the power of 4 space times space open parentheses negative fraction numerator 1 over denominator 2 x end fraction close parentheses space plus space 10 space times space x cubed space times space fraction numerator 1 over denominator 4 x squared space end fraction space plus space 10 space times space x squared space times space open parentheses negative fraction numerator 1 over denominator 8 x cubed end fraction close parentheses space plus space 5 space times space x space times space open parentheses fraction numerator 1 over denominator 16 x to the power of 4 end fraction close parentheses space plus space 1 space times space 1 space times space open parentheses negative fraction numerator 1 over denominator 32 space x to the power of 5 end fraction close parentheses


space space space space space space space space space space space space space space space space space space space space space space space bold equals bold space bold italic x to the power of bold 5 bold space bold minus bold space bold 5 over bold 2 bold italic x to the power of bold 3 bold space bold plus bold space bold 5 over bold 2 bold italic x bold space bold minus bold space fraction numerator bold 5 over denominator bold 4 bold x end fraction bold space bold plus bold space fraction numerator bold 5 over denominator bold 16 bold x to the power of bold 3 end fraction bold space bold minus bold space fraction numerator bold 1 over denominator bold 32 bold x to the power of bold 5 end fraction

 


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

અહીં, straight a space equals space 3 straight x comma space straight b space equals space minus 2 space અન ે space straight n space equals space 6 space.

આ કિંમતો દ્વિપદી પ્રમેયમાં મૂકતાં,

open parentheses 3 straight x space minus space 2 close parentheses to the power of 6 space equals space open parentheses table row 6 row 0 end table close parentheses open parentheses 3 x close parentheses to the power of 6 open parentheses negative 2 close parentheses to the power of 0 space plus space open parentheses table row 6 row 1 end table close parentheses open parentheses 3 x close parentheses to the power of 5 space open parentheses negative 2 close parentheses to the power of 1 space plus space open parentheses table row 6 row 2 end table close parentheses open parentheses 3 x close parentheses to the power of 4 open parentheses negative 2 close parentheses squared space plus space open parentheses table row 6 row 3 end table close parentheses open parentheses 3 x close parentheses cubed open parentheses negative 2 close parentheses cubed space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus space open parentheses table row 6 row 4 end table close parentheses open parentheses 3 x close parentheses squared space open parentheses negative 2 close parentheses to the power of 4 space plus space open parentheses table row 6 row 5 end table close parentheses open parentheses 3 x close parentheses to the power of 1 open parentheses negative 2 close parentheses to the power of 5 space plus space open parentheses table row 6 row 6 end table close parentheses open parentheses 3 x close parentheses to the power of 0 open parentheses negative 2 close parentheses to the power of 6

space 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 open parentheses 729 x to the power of 6 close parentheses space times space 1 space plus space 6 space times space open parentheses 243 x to the power of 5 close parentheses space times space open parentheses negative 2 close parentheses space plus space 15 space times space open parentheses 81 x to the power of 4 close parentheses space times space 4 space plus space 20 space times space open parentheses 27 x cubed close parentheses space times space open parentheses negative 8 close parentheses space plus space 15 space times space open parentheses 9 x squared close parentheses space times space 16

space space space space space space space space space space space space space space space space space space space space equals space 729 x to the power of 6 space minus space 2916 x to the power of 5 space plus space 4860 x to the power of 4 space minus space 4320 x cubed space plus space 2160 x squared space minus 576 x space space plus space 64

 


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