计算题4(a-b)²-(2a+b)(-b+2a)(x+2y-6)(x-2y+6)999²-1002×9982011+2011²-2012²(2+1)(2²+1)·…·(2的三十二次方+1)分解因式(x+3)(x+2)+x²-9(x-y)³+9(x-y)-6(x-y)²2(a²-2a+1)-b(a-1)(a²+b²-c²)²-4a²b²(x+2y)²-2(x+2y)+1(a+b)²-4(a+b-1)已知x²-y²=6,x+y=3 求x y 的值已知x-y=2,y-z=2,x+z=14 求x²-z²的值已知a≠b 且a(a+2)=b(b+2) 求a+b的值已知x(x+1)-(x²+y)=-3 ,求(x²+y²/2)-xy的值TAT

999²-1002×998=999^2-(999+3)(999-1)=999^2-999^2-2*999+3=-1997
2011+2011²-2012²=2011+(2011+2012)(2011-2012)=2011-2011-2012=-2012
(2+1)(2²+1)·…·(2的三十二次方+1)
=(2-1)(2+1)(2²+1)·…·(2的三十二次方+1)
=(2²-1)(2²+1)·…·(2的三十二次方+1)
=……
=(2的三十二次方-1)(2的三十二次方+1)
=(2的64次方-1)

(x+3)(x+2)+x²-9=（x+3)(x+2-x+3)=5(x+3)
(x-y)³+9(x-y)-6(x-y)²=(x-y)(x-y-3)^2
2(a²-2a+1)-b(a-1)=(a-1)(2a-2-b)
(a²+b²-c²)²-4a²b²=((a²+b²-c²)+2ab)((a²+b²-c²)-2ab)=(a+b+c）(a+b-c)(a-b+c)(a-b-c)
(x+2y)²-2(x+2y)+1=(x+2y-1)^2
(a+b)²-4(a+b-1)=(a+b-2)^2

4(a-b)²-(2a+b)(-b+2a) =4(a-b)²-(4a²-b²) = 4a²-8ab+4b²-(4a²-b²) = -8ab+5b² (x+2y-6)(x-2y+6)=x ²-(2y-6)²=x ²-(4y²-24y+36)=x ²-4y&...