Trinomial Expansion

( x + y+z )n = Σ(i,j,r) C(n, [i,j,r]) xi yjzr

where C(n, [i,j,r]) = n! /(i!j!r!)

or ( x + y+z )n =  j=nΣj=0 r=mΣr=0 ( nCj *  jCr ) zrx(n-m) y(m-r)

Value of     x
Value of     y
Value of     z
Value of     n
value of     i  (power of x)
Value of    j  (power of y)
Value of     r (power of z)
 

 

Total number of terms (n +1)(n+2)/2
Numerical value of expression ( x + y+z )n
Co-efficient of xiyjzr C(n, [i,j,r])
Value of x xi
Value of y yj
Value of z zr
Product of x , y & z xi yjzr
 Total value of rth term of z i.e. xiyjzr  C(n, [i,j,r]) xi yjzr
Sum of all Co-efficient in expansion  3n