Question

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

Answer 1

The number of terms in the expansion of (x + y + z)ⁿ `((n + 1)(n + 2))/2`.

Explanation:

The expression (x + y + z)ⁿ can be written a [x + (y + z)]ⁿ

∴ [x + y + z]ⁿ = ⁿC₀xⁿ (y + z)⁰ + ⁿC1(x)_n–1 (y + z) + ⁿC₂(x) ^n–2(y + z)² + … + ⁿCn(y + z)ⁿ

∴ Number of terms 1 + 2 + 3 + 4 + … (n + 1)

= `((n + 1)(n + 2))/2`