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(1).16 x3-24 x2 y2+12x y4-2 y6

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(1).16 x3-24 x2 y2+12x y4-2 y6
2(2x-y2)3
(2).a3+3a2 b+3b2 a-7b3
(a-b)(a2+4ab+7b2)
(3).x2-x-(y-3)(y-4)
(x-y+3)(x+y-4)
(4).x4+y4+(x+y)4
2(x2+xy+y2)2
另加5-15分!
(1).16 x3-24 x2 y2+12x y4-2 y6
(1).16 x3-24 x2 y2+12x y4-2 y6
=2(8x^3-12x^y^2+6xy^4-y^6)
=2
=2(2x-y^2)(4x^2-4xy^2+y^4)
=2(2x-y2)3
(2).a3+3a2 b+3b2 a-7b3
=(a^3-a^2b)+(4a^2b-4b^3)+(3b^2a-3b^3)
=(a-b)a^2+(a-b)(4ab+4b^2)+(a-b)3b^2
=(a-b)(a^2+4ab+7b^2)
(3).x2-x-(y-3)(y-4)
=x^2-x-y^2+7y-12
= x^2-y^2-x+7y-12
=(x+y)(x-y)-(x-7y)-12(用十字相乘法)
=(x-y+3)(x+y-4)
(4).x4+y4+(x+y)4
=x^4+y^4+x^4+4x^3y+6x^2y^2+4xy^3+y^4
=2(x^4+2x^3y+3x^2y^2+2xy^3+y^4)
=2
=2
=2(x^2+xy+y^2) (x^2+xy+y^2)
=2(x^2+xy+y^2)^2
打字打得好累啊.