(3x-2y)^2+(2x-3y)^2-125(x-y)分解因式

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(3x-2y)^2+(2x-3y)^2-125(x-y)分解因式
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(3x-2y)^2+(2x-3y)^2-125(x-y)分解因式
(3x-2y)^2+(2x-3y)^2-125(x-y)分解因式

(3x-2y)^2+(2x-3y)^2-125(x-y)分解因式
利用a^3+b^3=(a+b)(a^2-ab+b^2)=(a+b)((a-b)^2+ab)
其中125(x-y)^3=(5x-5y)^3
为方便计算令2x-3y=a;3x-2y=b;5x-5y=c且a+b=c;a-b=-(x+y)
=(a+b)((a-b)^2+ab))-c^3
=c((a-b)^2+ab-c^2)
=c((a-b)^2+ab-(a+b)^2)
=c((a-b+a+b)(a-b-a-b)+ab)
=c(2a*(-2b)+ab)
=c(-4ab+ab)=-c(3ab)=-3(5x-5y)(2x-3y)(3x-2y)
=-15(x-y)(2x-3y)(3x-2y)

(3x-2y)^2+(2x-3y)^2-125(x-y)
=9x^2+4y^2-12xy+4x^2+9y^2-12xy-125x+125y
=13x^2+13y^2-24xy-125x+125y

13x^2-24xy-125x+125y+13y^2

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