因式分解(1)4x^4-4x^2y^2+y^4+xy^3(2)a^2-b^2-x^2+y^2-2ay+2bx
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(1)4x^4-4x^2y^2+y^4+xy^3
=4x^2(x^2-y^2)+y^3(y+x)
=4x^2(x+y)(x-y)+y^3(x+y)
=(x+y)(4x^3-4x^2y+y^3)
(2)a^2-b^2-x^2+y^2-2ay+2bx
=(a^2-2ay+y^2)-(b^2-2bx+x^2)
=(a-y)^2-(b-x)^2
=(a-y+b-x)(a-y-b+x)
=4x^2(x^2-y^2)+y^3(y+x)
=4x^2(x+y)(x-y)+y^3(x+y)
=(x+y)(4x^3-4x^2y+y^3)
(2)a^2-b^2-x^2+y^2-2ay+2bx
=(a^2-2ay+y^2)-(b^2-2bx+x^2)
=(a-y)^2-(b-x)^2
=(a-y+b-x)(a-y-b+x)
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