Please expand :(x+y+z)^(n)

Question

Please expand :(x+y+z)^(n)

Answer 1

For this question, you can use the Multinomial Theorem (a version of the Binomial Theorem for three or more terms). Or, you can group the terms (as in, ((x+y) + z)ⁿ) and apply the Binomial Theorem as usual.

 

For example, (x+y+z)³ = ((x+y) + z)³ = (x+y)³ + 3(x+y)²z + 3(x+y)z² + z³

 

Then, expand the (x+y) terms using the Binomial Theorem:

 

(x³ + 3x²y + 3xy² + y³) + 3(x² + 2xy + y²)z + 3xz² + 3yz² + z³