Using properties of determinants, prove that
`|(x+y, x,x),(5x + 4y ,4x, 2x),(10x+8y,8x,3x)| = x^(3)`.

Using properties of determinant show that : |(y+z,x,x),(y,z+x,y),(z,z,x+y)|=4xyz

Using properties of determinant show that : |((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

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

Find x and y if :- [(x+3y, y),(7-x, 4)]=[(4, -1),(0, 4)] .

If x=3+2i ,then prove that x^4-4x^3+4x^2+8x+39=0 .

Resolve into factors : x^4 + x^2y^2 + y^4

If x-2y = 4 then prove that x^3-8y^3-24xy-64=0

Find x and y if :- [(x+3, 4),(y-4, x+y)]=[(5,4),(3,9)] .

Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)