" (9) "(x+y-2z)^(2)-x^(2)-y-y^(2)-3z^(2)+4xy

Simplify each of the following expressions: (x+y+z)^(2)+(x+(y)/(2)+(z)/(3))^(2)-((x)/(2)+(y)/(3)+(z)/(4))^(2)(x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy-(x^(2)+x+1)^(2)-(x^(2)+x+1)^(2)

Simplify: (x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy

Simplify: (x+y-2z)^2-x^2-y^2-3z^2+4x y

Find the following produts: (i) (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2xz)(2x-y+2z)(4x^(2)+y^(2)+9z^(2)+2xy+3yz-6xz)

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

if x^(4) -y^(4)-x^(2)y^(2)-2xy^(3)= z^(6) then prove that log_(z)(x^(2) -y^(2)-xy) + log_(z) (x^(2) +y^(2) +xy) =6