Question

The coefficients of how many terms in the expansion of (x + y – z)^100 are negative?

Answer 1

Answer:

there is only 1 negative coefficient that is ( -1) of

( -z )

Answer 2

Answer:

Number of terms in a multinomial of the form (x+y+z)ⁿ = n+r-1Cr-1

r= number of variables present in multinomial

Number of terms in (x+y+z)¹⁰⁰

n=100 r=3

¹⁰⁰⁺³⁻¹C₃₋₁ = ¹⁰²C₂ = 102!/100!*2! = 101*102/2 = 101*56 = 5656 terms

So (x+y+z)¹⁰⁰ has ¹⁰²C₂=5656 terms in its expansion .