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Factorise 4x^2+y^2+z^2-4x y-3y z+4x z....

Factorise `4x^2+y^2+z^2-4x y-3y z+4x z`.

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To factorize the expression \(4x^2 + y^2 + z^2 - 4xy - 3yz + 4xz\), we can follow these steps: ### Step 1: Rewrite the expression Start by rewriting the expression clearly: \[ 4x^2 + y^2 + z^2 - 4xy - 3yz + 4xz \] ...
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Knowledge Check

  • Find the intersection of the spheres x^2+y^2+z^2+7x-2y-z=13 and x^2+y^2+z^2+3x+3y+4z=8.

    A
    `x-y-z=1`
    B
    `x-2y-z=1`
    C
    `x-y-2z=1`
    D
    `2x-y-z=1`

  • The shortest distance from the plane 12x+4y+3z=327 to the sphere x^2+y^2+z^2+4x-2y-6z=155 is

    A
    26
    B
    `11(4)/13`
    C
    13
    D
    39

  • The intersection of the spheres x^2+y^2+z^2+7x-2y-z=1 and x^2+y^2+z^2-3x+3y+4z=-4 is

    A
    `2x-y-z=1`
    B
    `-2x+y+z=1`
    C
    `2x-y+z=1`
    D
    `2x+y+z=1`

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