化简:(X^2+XY+Y^2)^2-4XY(X^2+Y^2){x^2-xy+y^2}^2 我想知道怎么化简得来的?

来源：学生作业帮助网编辑：作业帮时间：2024/11/20 18:44:04

$化简:(X^2+XY+Y^2)^2-4XY(X^2+Y^2){x^2-xy+y^2}^2 我想知道怎么化简得来的?$

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化简:(X^2+XY+Y^2)^2-4XY(X^2+Y^2){x^2-xy+y^2}^2 我想知道怎么化简得来的?
化简:(X^2+XY+Y^2)^2-4XY(X^2+Y^2)
{x^2-xy+y^2}^2 我想知道怎么化简得来的?

化简:(X^2+XY+Y^2)^2-4XY(X^2+Y^2){x^2-xy+y^2}^2 我想知道怎么化简得来的?
令X^2+Y^2=a XY=b
(a+b)^2-4ab=a^2+b^2+2ab-4ab=a^2+b^2+-2ab=(a-b)^2
(X^2+XY+Y^2)^2-4XY(X^2+Y^2)={x^2-xy+y^2}^2

(X^2+XY+Y^2)^2-4XY(X^2+Y^2)
=X^4+X^2Y^2+Y^4+2YX^3+2X^2Y^2+2XY^3-4YX^3-4XY^3
=X^4+X^2Y^2+Y^4-2YX^3+2X^2Y^2-2XY^3
=(x^2-xy+y^2)^2
最后一步是根据公式而来

化简：3x^2-[5xy-(x^y-3xy)+4x^2y-8xy] 化简x^-y^/x^-2xy+y^ 化简2(x²y+xy)-3(x²y-xy)-4x²y 化简：2x²y+{2xy-[3x²y-2(-3x²y+2xy)]-4xy}化简：2x²y+{2xy-[3x²y-2(-3x²y+2xy)]-4xy} [(x-y)^2-(x+y)^2]/(-4xy) 化简因式分解:12xy^2(y-x)+xy^3(x-y)+4x^2y(x-y) 化简:[4xy(x-y)^-1 + (xy^-1 - x^-1y)/(x^-1 + y^-1)] / (x+y)^2 (x^2+2xy+y^2-4xy)*(x^2-2xy+y^2+4xy) (x+y)(x+y+2xy)+(xy+1)(xy-1)(x+y)(x-y)+4(y-1) 5x^2y-3xy^2+4xy-14xy^2+4xy-2x^2y（化简） (x^-4y^)/(x^+2xy+y^)/(x+2y)/(2x^+2xy) 因式分解 x-xy+3y-3x 2x+xy-y-4x+5y-6 （-3x^y+2xy)-( )=4x^+xy （x^2+xy/x-y)/（xy/x-y)计算 x^2y-2xy+y化简化简4xy-3y²-3x²+xy-3xy-2x²+x²-2y² 2x(x-y)+4xy(y-x) 因式分解2x(x-y)+4xy(y-x) 因式分解化简：x-y/x+3y÷x^-y^2/x^2+6xy+9y^2-(xy/x+y)