गुणनखंड करें - 4x² + y² + z² - 4xy - 2yz + 4xz (ii) 4x² + 9y² + 16z² + 12xy - 24yz - 16xz (iii) x² + 4y² + z² + 4xy - 4yz - 2zx (iv) 4x² + 9y² + 4z² - 12xy - 12yz + 8zx 1/4x² + y² + 1/16z² - xy - 1/2yz + 1/4zx

यहाँ $A^2 = \frac{1}{4}x^2$, $B^2 = y^2$, $C^2 = \frac{1}{16}z^2$ है।
$2AB = -xy \implies A=\frac{1}{2}x, B=-y$ (या $A=-\frac{1}{2}x, B=y$)
$2BC = -\frac{1}{2}yz \implies B=-y, C=\frac{1}{4}z$
$2CA = \frac{1}{4}zx \implies C=\frac{1}{4}z, A=\frac{1}{2}x$
इसलिए, $A=\frac{1}{2}x, B=-y, C=\frac{1}{4}z$ है।