2x^2-xy-15y^2+6x+4y-4a^4+b^4

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2x^2-xy-15y^2+6x+4y-4a^4+b^4
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2x^2-xy-15y^2+6x+4y-4a^4+b^4
2x^2-xy-15y^2+6x+4y-4
a^4+b^4

2x^2-xy-15y^2+6x+4y-4a^4+b^4
待定系数法:
设:2x^2-xy-15y^2+6x+4y-4 = (2x+ay+b)(x+cy+d)
(2x+ay+b)(x+cy+d)=2x^2+(a+2c)xy+acy^2+(b+2d)x+(ad+bc)y+bd
对比系数得到方程组,无解.
如果常数项-4改成4就有解
2x^2-xy-15y^2+6x+4y-4 = (2x+5y+2)(x-3y+2)-8
a^4+b^4
=a^4+b^4 +2a²b²-2a²b²
=(a²+b²)²-2a²b²
=[(a²+b²)+√2*ab][(a²+b²)-√2*ab]
=(a²+b²+√2*ab)(a²+b²-√2*ab)