Factorise $4x^{2}y^{2}z - 8xy^{3}z^{2} + 12x^{3}yz$.

Factorise $4x^{2}y^{2}z - 8xy^{3}z^{2} + 12x^{3}yz$.
  1. $4xyz(xy - 2y^{2}z + 3x^{2})$
  2. $4xyz(xy + 2y^{2}z + 3x^{2})$
  3. $2xyz(2xy - 4y^{2}z + 6x^{2})$
  4. $xyz(4xy - 8y^{2}z + 12x^{2})$

Solution

GCD numerically is 4 and the lowest powers of $x,y,z$ in every term are $x,y,z$. Factor: $4xyz(xy - 2y^{2}z + 3x^{2})$.

Asked in: IMO

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