Question

$(x - 2y - z)^{3}$
expand using identities

Answer 1

(x-2y-z)^{3}
= (x-2y-z)(x-2y-z)(x-2y-z)
= x[(x-2y-z)(x-2y-z)]-2y [(x-2y-z)(x-2y-z)]-z [(x-2y-z)(x-2y-z)]
= x [x (x-2y-z)-2y(x-2y-z)-z (x-2y-z)] -2y[x(x-2y-z)-2y (x-2y-z)-z (x-2y-z)]-z [x(x-2y-z)-2y (x-2y-z)-z (x-2y-z)]
= x [x^2-2xy-xz-2xy+4y^2+2yz-xz+2yz+z^2]-2y [x^2-2xy-xz-2xy+4y^2+2yz-xz+2yz+z^2]-z [x^2-2xy-xz-2xy+4y^2+2yz-xz+2yz+z^2]
= x [x^2-4xy-2xz+4y^2+4yz+z^2]-2y [x^2-4xy-2xz+4y^2+4yz+z^2]-z [x^2-4xy-2xz+4y^2+z^2]
= x^3-4x^2y-2x^2z+4xy^2+4xyz+xz^2-2x^2y+8xy^2+4xyz-8y^3-8y^2z-2yz^2-x^2z+4xyz+2xz^2-4y^2z-4yz^2+z^3
= x^3-6x^2y-3x2z+12xy^2+12xyz+3xz^2-8y^3-12y^2z-6yz^2+z^3 answer