先化简,再求值.2x(x+y)-(x+y)^2,其中x=根号2012,y=根号2011(2)a^2(x-y)-2a(x-y)^2+(x-y)^3

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先化简,再求值.2x(x+y)-(x+y)^2,其中x=根号2012,y=根号2011(2)a^2(x-y)-2a(x-y)^2+(x-y)^3

先化简,再求值.2x(x+y)-(x+y)^2,其中x=根号2012,y=根号2011(2)a^2(x-y)-2a(x-y)^2+(x-y)^3
先化简,再求值.2x(x+y)-(x+y)^2,其中x=根号2012,y=根号2011
(2)a^2(x-y)-2a(x-y)^2+(x-y)^3

先化简,再求值.2x(x+y)-(x+y)^2,其中x=根号2012,y=根号2011(2)a^2(x-y)-2a(x-y)^2+(x-y)^3

2x(x+y)-(x+y)²
=(x+y)[2x-(x+y)]
=(x+y)(x-y)
=x²-y²
=(√2012)²-(√2011)²
=2012-2011
=1
a²(x-y)-2a(x-y)²+(x-y)³
=(x-y)[a²-2a(x-y)+(x-y)²]
=(x-y)[a-(x-y)]²
=(x-y)(a-x+y)²

(1)2x(x+y)-(x+y)^2=(x+y)(2x-x-y)=(x+y)(x-y)=x²-y²=(√2012)²-(√2011)²=2012-2011=1
(2)a^2(x-y)-2a(x-y)^2+(x-y)^3=(x-y)[a²-2a(x-y)+(x-y)²]=(x-y)[a-(x-y)]²=(x-y)(a-x+y)²