XY ^ 4 + YZ ^ 4 + ZX ^ 4-xz ^ 4-yx ^ 4-zy ^ 4 factorization I've seen three factors (X-Y) (Y-Z) (z-x) What's next?

The remaining factor is (XX + YY + ZZ + XY + YZ + ZX)
The original and decomposed factors are XYZ rotation, so the remaining factors must be the quadratic rotation of XYZ, that is, the form of M (XX + YY + zz) + n (XY + ZY + ZX), where m and N are coefficients. From the coefficients of the original, it is not difficult to see that the absolute values of M and N must be 1. Just try it

RELATED INFORMATIONS

1. The last digit of the result of formula 1991 * 1993 * 1995 * 1999-1992 * 1994 * 1996 * 1998 is -? The last digit of the result of 1991 * 1993 * 1995 * 1999-1992 * 1994 * 1996 * 1998 is -?
2. As shown in the figure, in the plane rectangular coordinate system, the quadrilateral ABCD is an isosceles trapezoid, where the coordinate of point B is (- 1,0), and point a is seated
3. If the points corresponding to complex numbers 3 + I and 2 + 3I in the complex plane are p and Q respectively, the complex number corresponding to vector PQ is () A. 5+4iB. 1-2iC. -1+2iD. 1+2i
4. Is it wrong or correct that the complex number represented by a vector remains unchanged after the translation of the vector? For example, I read a sentence in a book that "no matter where the vector is translated, the complex number it represents is the same". I don't understand it. For example, the complex number represented by the vector (1,1) is 1 + I. after the vector is translated 2 units along the X axis, the complex number it represents should be 3 + I. how can it remain unchanged?
5. Rotate the vector corresponding to the complex z = 2-I 90 degrees counter clockwise, what is the corresponding complex number In addition, tell me the vector corresponding to the complex z = 2-I
6. A sufficient and necessary condition for Z ∈ R is that z = Z conjugate? Right? And a sufficient and necessary condition for Z to be an imaginary number is that Z + Z conjugate belongs to R pair RT
7. If Z is an imaginary number and (Z-2) / (Z & sup2; + 1) belongs to R, find the locus of the point corresponding to Z in the complex plane
8. The complex number is known as Z = sin θ + (2-cos ^ 2 θ) I, 0 ≤ θ 1. The complex number is known as Z = sin θ + (2-cos ^ 2 θ) I, 0 ≤ θ
9. Why do we set z = cos α + sin β I in some high school plural questions, and if | Z-2 | = 2, why set 2 + cos α + sin α I QAQ, the concept is a little vague,
10. I hope someone can answer, θ∈ R, z = (a + cos θ) + (2A - sin θ) I If the modulus of complex z = (a + cos θ) + (2A - sin θ) I does not exceed 2 for all θ∈ R, then the value range of real number a is_______ .
11. Rotate the line y = root 3x around the origin by 30 ° counterclockwise, and what is the inclination angle a = of the line
12. There are several ways to make a big rectangle out of 60 squares of the same size
13. What is the period of y = 2Sin Λ X-1? Odd function or even function?
14. On the round dining table with a diameter of 2 meters and a height of 1 meter, a square tablecloth is laid. The four corners of the tablecloth just touch the ground. The area of this tablecloth is () square meter.
15. Calculation of anomalous integral: ∫ (1,2) 1 / [x (LNX) ^ 2] DX= Where 1 is the lower limit and 2 is the upper limit,
16. A bathroom is 1.8 meters long and 1.44 meters wide. Now we need to lay square tiles on the bathroom floor. How many centimeters is the maximum side length of square tiles?
17. Let the population x ~ U (0, θ), x1, X2, ···, xn be a sample taken from the population, and x0 be the average number of samples (1) It is proved that θ 1 = 2x0, θ 2 = (n + 1) / N. x (n) is an unbiased estimate of θ (where x (n) = max {x1, X2, ···, xn}); (2) Which one of theta 1 and theta 2 is more effective (n ≥ 2)?
18. A square steel plate, 9 / 8 meters in circumference, its area is () square decimeters
19. If the sequence {xn} satisfies lgxn + 1 = 1 + lgxn and X1 + x2 + +If X100 = 100, LG (X101 + X102 +...) +x200）=（　　） A. 102B. 100C. 1000D. 101
20. After the circle is cut into an approximate rectangle, the perimeter is increased by 8 cm, and the perimeter and area of the circle are calculated