化简求值: [(x+2y)2-(x-2y)2-(x+2y)(x-2y)-4y2]÷2x,其中x=-2,y=1/2.

问题描述:

化简求值:
[(x+2y)2-(x-2y)2-(x+2y)(x-2y)-4y2]÷2x,其中x=-2,y=

1
2

[(x+2y)2-(x-2y)2-(x+2y)(x-2y)-4y2]÷2x,
=[(x2+4xy+4y2)-(x2-4xy+4y2)-(x2-4y2)-4y2]÷2x,
=(x2+4xy+4y2-x2+4xy-4y2-x2+4y2-4y2)÷2x,
=(-x2+8xy)÷2x,
=-

1
2
x+4y,
当x=-2,y=
1
2
时,
原式=-
1
2
×(-2)+4×
1
2
=1+2=3.