Question

①先化简，再求值：（﹣2y－x）（2y－x）－（x＋2y）²，其中x=1，y=2;

②已知(x＋y）²=80,（x－y）²=60，求x²＋y²及xy的值

Answer 1

（﹣2y－x）（2y－x）－（x＋2y）²
=(x-2y)(x+2y)-(x+2y)²
=(x+2y)(x-2y-x-2y)
=(x+2y)(-4y)
=-4y(x+2y)
=-4*2*(1+4)
=-40

(x+y)²-(x-y)²=(x+y+x-y)(x+y-x+y)=4xy=80-60=20
xy=5

(x+y)²=x²+2xy+y²=x²+y²+10=80
x²+y²=70

Answer 2

（﹣2y－x）（2y－x）－（x＋2y）²
=(x-2y)(x+2y)-(x+2y)²
=(x+2y)(x-2y-x-2y)
=(x+2y)(-4y)
=-4y(x+2y)
=-4*2*(1+4)
=-40

(x+y)²-(x-y)²=(x+y+x-y)(x+y-x+y)=4xy=80-60=20
xy=5

(x+y)²=x²+2xy+y²=x²+y²+10=80
x²+y²=70

Answer 3

-8y^2-4xy=-40