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①计算:(﹣x 2 +2xy﹣y 2 )﹣2(xy﹣3x 2 )+3(...

解:原式=6xy﹣9x 2 y﹣6xy+3x 2 y=﹣6x 2 y.

解:原式=3x 2 y﹣(2x 2 y﹣6xy+3x 2 y﹣xy)=3x 2 y﹣2x 2 y+6xy﹣3x 2 y+xy=﹣2x 2 y+7xy.

(1) (x-y)(x^2-xy+y^2)+xy(y-x) =(x-y)(x^2-xy+y^2)-xy(x-y) =(x-y)(x^2-xy+y^2-xy) =(x-y)(x^2-2xy+y^2) =(x-y)(x-y)^2 =(x-y)^3 (2)-2xy-4x^2y+2xy^2 =-2xy(1+2x-y) (3)3x^2(a+3)-4x^2y(a+3) =x^2(a+3)(3-4y) a^2-3a+2 =(a-2)(a-1)

原式=-3x2+6xy-3y2-2y2-6xy+8x2=(-3+8)x2+(6-6)xy-(3+2)y2=5x2-y2.

(1)①A+B+C=x2-3xy+y2-2xy-x2+2y2=-5xy+3y2;②2A-B-2C=2(x2-3xy)-(y2-2xy)-2(-x2+2y2)=2x2-6xy-y2+2xy+2x2-4y2=4x2-4xy-5y2;(2)2(3x2y-xy2)-(xy2+6x2y)+1=6x2y-2xy2-xy2-6x2y+1=-3xy2+1,∵|x-1|+(y+2)2=0,∴x=1,y=-2,则原式=-...

2(3x2-2xy+4y2)-3(2x2-xy+2y2),=6x2-4xy+8y2-(6x2-3xy+6y2),=6x2-4xy+8y2-6x2+3xy-6y2,=-xy+2y2;当x=2,y=-1时,原式=-2×(-1)+2×(-1)2=2+2=4.

(3x2y-2xy2)-2(x2y-3xy2)-(3x2y-2xy2)=3x2y-2xy2-2x2y+6xy2-3x2y+2xy2)=-2x2y+6xy2,当x=-4,y=-12时,原式=-2×(-4)2×(-12)+6×(-4)×(?12) 2=16+(-6)=10.

3x2-2xy+12y2=47① 2x2+xy+8y2=36② ①*36-②*47,得14x^2-119xy+56y^2=0, 2x^2-17xy+8y^2=0, (x-8y)(2x-y)=0, ∴x=8y,③或y=2x④ 由①③解得(x,y)=(4,1/2),(-4,-1/2); 由①④解得(x,y)=(1,2),(-1,-2). ∴x^2+4y^2=17, x^2-4y^2=土15, 于是x^4-16y^4=土255.

原式=3x2-3xy+6y2-2x2+4xy-4y2=x2+xy+2y2.当x=-2,y=12时,原式=(-2)2+(-2)×12+2×(12)2=72.

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