作业帮(z²-x²-y²)²-4x²y²分解因式
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/18 09:08:40
(z²-x²-y²)²-4x²y²分解因式
(z²-x²-y²)²-4x²y²分解因式
(z²-x²-y²)²-4x²y²分解因式
(z²-x²-y²)²-4x²y²
= (z²-x²-y² + 2xy)(z²-x²-y² - 2xy)
= {z² - (x²+y² - 2xy)} * {z² - (x²+y² + 2xy)}
= {z² - (x-y)² } * {z² - (x+y)² }
= (z+x-y)(z-x+y) * (z+x+y)(z-x-y)
= (x+y+z)(x-y+z)(-x+y+z)(-x-y+z)
(z²-x²-y²)²-4x²y²=(z²-x²-y²-2xy)(z²-x²-y²+2xy)
=[z²-(y＋x)²][z²-(x-y)²]
＝(z＋y＋x)(z－y－x)(z－x+y)(z+x－y)