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
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