Show that the term containing x3 does not exist in the expansion of (3x-1+2x)8 - Maths - Binomial Theorem

Question

Show that the term containing x3 does not exist in the expansion of
(3x-1+2x)8

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Assuming that question is3x - 12x8Now,General term isTr+1=cr8 3x8-r -12xr=cr8 
 38-r   x8-r   -12r 1xr=cr8 
 38-r   x8-r   -12r x-r=cr8 
 38-r   x8-2r 
 -12rFor x38-2r=3-2r=3-8-2r=-5r=52r can only have integral value
So , there is no value of r for term x3 
Thus, x3 does not exists in the expansion 3x - 12x8 
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Show that the term containing x3 does not exist in the expansion of (3x-1+2x)8.