分解因式 x^4-3x²y²+2y^4
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 13:04:13
![分解因式 x^4-3x²y²+2y^4](/uploads/image/z/2547303-15-3.jpg?t=%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F+x%5E4-3x%26%23178%3By%26%23178%3B%2B2y%5E4)
分解因式 x^4-3x²y²+2y^4
分解因式 x^4-3x²y²+2y^4
分解因式 x^4-3x²y²+2y^4
x^4-3x²y²+2y^4
=(x²-2y²)(x²-y²)
=(x-√2y)(x+√2y)(x-y)(x+y)
x^4-3x²y²+2y^4
用十字相乘法:
x^2 -y^2
\ /
/\
x^2 / \ -2y^2
得:
x⁴-3x²y²+2y⁴=(x²-y²)(x²-2y²)=(x+y)(x-y)(x+√2y)(x-√2y)
原式=(x²-y²)(x²-2y²)=(x+y)(x-y)(x+√2y)(x-√2y)