x²+y²-x²y²-4xy-1因式分解

x²+y²-x²y²-4xy-1因式分解
x²+y²-x²y²-4xy-1因式分解

x²+y²-x²y²-4xy-1因式分解
怎么这个也不会啊,不是有例题吗?注意多看例题和要点精析,里面有一些是补充内容,平时不曾或很少用到,到了高中就要求熟练的,里面注意一些没有却在解题过程中要用到的一些定理.

x²+y²-x²y²-4xy-1
=x²-2xy+y²-x²y²-2xy-1
=(x-y)²-（xy-1)²
=（x-y+xy-1)(x-y-xy+1)
=(x-1)(y+1)(x+1)(y-1)

x²+y²-x²y²-4xy-1
=(x²-2xy+y²)-(x²y²+2xy+1) (分解)
=(x-y)²-(xy+1)² (两个完全平方式)
=(x-y+xy+1)(x-y-xy-1) (平方差)

x² + y² - x²y² - 4xy - 1
= (x² + y² - 2xy) - (x²y² + 2xy + 1)
= (x - y)² - (xy + 1)²
= (x - y + xy + 1)(x - y - xy - 1)