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[" Using properties of determinants,prove that "|[x+2y,x,x+y],[x+y,x+2y,x]|],[9y^(2)(x+y),[" Delhi "2017," AI "2013]],[|[a,-1,0]|]

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Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,x,y]]=-2(x^3+y^3)

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)|=x^3

By using properties of determinant prove that |(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0