Question

已知x+y+z=0,使求(x的平方-y的平方-z的平方)平方-4y的平方z的平方的值

Answer 1

(x的平方-y的平方-z的平方)平方-4y的平方z的平方
=(x²-y²-z²)²-(2yz)²
=(x²-y²-z²+2yz)(x²-y²-z²-2yz)
=[x²-(y-z)²][x²-(y+z)²]
=(x+y-z)(x-y+z)(x+y+z)(x-y-z)
∵x+y+z=0
∴原式=0

Answer 2

(x^2－y^2－z^2)^2－4y^2z^2
＝(x^2－y^2－z^2)^2－(2yz)^2
＝(x^2－y^2－z^2＋2yz)(x^2－y^2－z^2－2yz)
＝[x^2－(y－z)^2][x^2－(y＋z)^2]
＝(x＋y－z)(x－y＋z)(x＋y＋z)(x－y－z)
＝0