已知x+y=7,x-y=5,求x2-y2-2y+2x的值.

问题描述:

已知x+y=7,x-y=5,求x2-y2-2y+2x的值.

x2-y2-2y+2x
=(x+y)(x-y)-2(y-x)
=(x+y)(x-y)+2(x-y)
=(x-y)(x+y+2),
将x+y=7,x-y=5,代入上式得:
原式=(x-y)(x+y+2)=5×9=45.