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分解因式:(1)y^2(x^2-2x)^3+y^2 (2)6x^2-7xy-3y^2 (3)x^2-4mx+8mn-4n^2
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(1)y^2(x^2-2x)^3+y^2=y^2(x^2-2x+1)=y^2*(x-1)^2
(2)6x^2-7xy-3y^2 =(2x-3y)(3x+y)
(3)x^2-4mx+8mn-4n^2=(x^2-4mx+4m^2)-(4m^2-8mn+4n^2)=(x-2m)^2-4(m-n)^2
=(x-2m-2(m-n))(x-2m+2(m-n))
=(x-4m+2n)(x-2n)
(2)6x^2-7xy-3y^2 =(2x-3y)(3x+y)
(3)x^2-4mx+8mn-4n^2=(x^2-4mx+4m^2)-(4m^2-8mn+4n^2)=(x-2m)^2-4(m-n)^2
=(x-2m-2(m-n))(x-2m+2(m-n))
=(x-4m+2n)(x-2n)
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