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)
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 |