Using properties of determinants. Prove that`|alphaalpha^2beta+gammarhorho^2gamma+alphagammagamma^2alpha+beta|=(rho-gamma)(gamma-alpha)(alpha-rho)(alpha+rho+gamma)`

Using properties of determinants.Prove that det[[alpha,alpha^(2),beta+alpharho,rho^(2),gamma+alphagamma,gamma^(2),alpha+beta]]=(rho-gamma)(gamma-alpha)(alpha-rho)(alpha+rho+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)

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)

Show that |[1,alpha,alpha^2],[1,beta,beta^2],[1,gamma,gamma^2]|=(alpha-beta)(beta-gamma)(gamma-alpha)

Using properties of determinant 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)

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)

|{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)(beta-gamma)(gamma-alpha)

Using properties of determinants, prove the following |(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)