Using peoperties of determinants in questions 11 to 15, prove that :
`|{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2),gamma+alpha),(gamma,gamma^(2),alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha-beta+gamma)`

Using properties of determinants in Exercise 11 to 15 prove that |{:(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha+beta+gamma)(alpha-beta)

Using properties of determinants prove that : {:|( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) |:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )

Using properties of determinants in Exercises prove that : {:[( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) ]:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )

Using properties of determinants in Exercises prove that : {:|( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) |:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )

Using properties of determinants. Prove that |(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta)|=(beta-gamma)(gamma-alpha)(alpha-beta)(alpha+beta+gamma)

Using properties of determinants, prove that: |[alpha,alpha^2,beta+gamma],[beta,beta^2,gamma+alpha],[gamma,gamma^2,alpha+beta]| = (beta-gamma)(gamma-alpha)(alpha-beta)(alpha+beta+gamma)

Using properties of determinants, prove that |[alpha, alpha^2, beta+gamma],[beta,beta^2,gamma+alpha],[gamma,gamma^2,alpha+beta]|=(beta-gamma)(gamma-alpha)(alpha-beta)(alpha+beta+gamma)

Prove that, |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta):}|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)