(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:2024/07/05 21:02:15
![(z²-x²-y²)²-4x²y²分解因式](/uploads/image/z/1813127-23-7.jpg?t=%28z%26%23178%3B-x%26%23178%3B-y%26%23178%3B%29%26%23178%3B-4x%26%23178%3By%26%23178%3B%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F)
(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)