把多项式(1-x²)(1-y²)-4xy分解因式的结果是(xy+m)(xy-1-x-y),则m=__
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![把多项式(1-x²)(1-y²)-4xy分解因式的结果是(xy+m)(xy-1-x-y),则m=__](/uploads/image/z/3802518-54-8.jpg?t=%E6%8A%8A%E5%A4%9A%E9%A1%B9%E5%BC%8F%281-x%26%23178%3B%29%281-y%26%23178%3B%29-4xy%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%E7%9A%84%E7%BB%93%E6%9E%9C%E6%98%AF%28xy%2Bm%29%28xy-1-x-y%29%2C%E5%88%99m%3D__)
把多项式(1-x²)(1-y²)-4xy分解因式的结果是(xy+m)(xy-1-x-y),则m=__
把多项式(1-x²)(1-y²)-4xy分解因式的结果是(xy+m)(xy-1-x-y),则m=__
把多项式(1-x²)(1-y²)-4xy分解因式的结果是(xy+m)(xy-1-x-y),则m=__
m=-1
快速突破法:
只看常数项
(1-x²)(1-y²)-4xy中展开后的常数为1*1=1
那么(xy+m)(xy-1-x-y)展开后的常数也一定为1
即m*(-1)=1
m=-1
解:(1-x^2)(1-y^2)-4xy=1-x^2-y^2+(xy2)^-4xy,且(xy+m)(xy-1-x-y)=(xy)^2-xy-x^2y-xy^2+mxy-m-mx-my,所以-m=1,所以m=-1。