The number of terms in the expansion of (x+y+z)power n

Open in App

Solution

Dear Student,
BY BINOMIAL EXPANSION:

(x+a)ⁿ=nC₀xⁿa⁰+nC₁x^n-1a¹+nC₂x^n-2a²+..........+nC_nx⁰aⁿ

No. of terms in (x+y+z)^n
⇒[x+(y+z)]^n
⇒[x+(y+z)]^n=nC₀xⁿ (y+z)⁰+nC₁x^n-1(y+z)¹+nC₂x^n-2(y+z)²+.....nC_nx⁰(y+z)ⁿ
=>No. of terms in (x+y+z)ⁿ
⇒(n+1)/2*[(n+2)/2]
⇒(n+1)/2(n+2)/2

Regards
Manshi Arora

Suggest Corrections

Similar questions

(x + y + z)^{n}

(x + y + z)^{5}

(x + y + z)^{n}

^{n + 2} C_{2}

One of the terms in the expansion of $(x + y)^{n}$ is $k x^{8} y^{13}$ . Find the number of terms in the expansion.

(x + y + z + w)^{n}

(x + y)^{n}

Join BYJU'S Learning Program