Question

若|x+y-1|+（x-y-2)²=0,求代数式（x+2y)(x-2y）-（2x-y)(-y-2x)的值.

Answer 1

x+y=1

x-y=2

(x+2y)(x-2y)-(2x-y)(-y-2x)

=(x+2y)(x-2y)+(2x-y)(y+2x)

=x²-4y²+4x²-y²

=5x²-5y²

=5(x+y)(x-y)

=10