`(3x - 2y + z)^2 - ( 3x + 2y - z)^2`

3x - [4y - {7x - (3z - 2y) + 4z - 3(x + 3y - 2z)}]

The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

Add: 5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

Prove that the lines 3x + 2y + z – 5 = 0 = x + y – 2z – 3 and 2x – y – z = 0 = 7x + 10y – 8z – 15 are perpendicular

Add : x y ^(2) z ^(2)+ 3x ^(2) y ^(2) z - 4x ^(2)yz ^(2), - 9x ^(2) y ^(2) z + 3x y ^(2) z ^(2) + x ^(2) yz ^(2)

If x + y + z = 6 and x^2 + y^2 + z^2= 20 then the value of x^3 + y^3 + z^3 - 3xyz is

Add the following: (i) x – 3y – 2z , 5x + 7y – 8z , 3x – 2y + 5z