已知x-y=1,求[(x+2y)2+(2x+y)(x-4y)-3(x+y)(x-y)]÷y的值.

问题描述:

已知x-y=1,求[(x+2y)2+(2x+y)(x-4y)-3(x+y)(x-y)]÷y的值.

原式=(x2+4xy+4y2+2x2-7xy-4y2-3x2+3y2)÷y
=(-3xy+3y2)÷y,
=-3x+3y,
=-3(x-y);
∵x-y=1,
∴原式=-3(x-y)=-3.