把下列各式因式分解。(1)x^3+3x^2+3x+9;(2)2x^2+xy-y^2-4x+5y-6
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(1)x^3+3x^2+3x+9
=x^2(x+3)+3(x+3)
=(x^2+3)(x+3)
(2)2x^2+xy-y^2-4x+5y-6
=(2x-y)(x+y)-4x+5y-6
=(2x-y)(x+y)+(2x+2y)-6x+3y-6
=(2x-y)(x+y)+2(x+y)-6x+3y-6
=(x+y)(2x-y+2)-3(2x-y+2)
=(2x-y+2)(x+y-3)
=x^2(x+3)+3(x+3)
=(x^2+3)(x+3)
(2)2x^2+xy-y^2-4x+5y-6
=(2x-y)(x+y)-4x+5y-6
=(2x-y)(x+y)+(2x+2y)-6x+3y-6
=(2x-y)(x+y)+2(x+y)-6x+3y-6
=(x+y)(2x-y+2)-3(2x-y+2)
=(2x-y+2)(x+y-3)
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