已知2x+y=4,求代数式[(x+y)2-(x-y)2-2y(x-1/2y)]÷4y的值.

问题描述:

已知2x+y=4,求代数式[(x+y)2-(x-y)2-2y(x-

1
2
y)]÷4y的值.

原式=[x2+y2+2xy-x2-y2+2xy-2xy+y2]÷4y
=(2xy+y2)÷4y
=

1
4
(2x+y)
=
1
4
×4
=1.