Question

因式分解(y+1）^4+(y+3)^4-272

Answer 1

(y+2-1)^4+(y+2+1)^4-272
令x=y+2
原式=(x-1)^4+(x+1)^4-272
2(x^4+6x^2+1)-272
=2(x^4+6x^2-135)
=2(x^2-9)(x^2+15)
=2(x+3)(x-3)(x^2+15)
=2(y+5)(y-1)(y^2+4y+19)

追问

第二步不懂

追答

1.
6x^2+xy-2y^2+2x-8y-8
=(2x-y)(3x+2y)+2(x-4y)-8
=(2x-y-2)(3x+2y+4)

2.
x^3-3x^2-13x+15
=x^3-3x^2+2x-15x+15
=x(x^2-3x+2)-15(x-1)
=x(x-2)(x-1)-15(x-1)
=(x-1)[x(x-2)-15]
=(x-1)[x^2-2x-15]
=(x-1)(x-5)(x+3)

3.
(y+2-1)^4+(y+2+1)^4-272
令x=y+2
原式=(x-1)^4+(x+1)^4-272
2(x^4+6x^2+1)-272
=2(x^4+6x^2-135)
=2(x^2-9)(x^2+15)
=2(x+3)(x-3)(x^2+15)
=2(y+5)(y-1)(y^2+4y+19)

4.
x^4+x^2y^2+y^4
=x^4+2x^2y^2+y^4-x^2y^2
=(x^2+y^2)^2-x^2y^2
=(x^2+y^2+xy)(x^2+y^2-xy)

追问

第二步不懂

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