Question

求几题解法，（因式分解）急~~

有过程。
1.(x²+4x+3）（x²+12x+35）+15
2.（a²+19a）²-408（a²+19a0-124848
3.(ab-1)²+（a+b-2）（a+b-2ab）
4.xy（x²-y²）+yz（y²-z²）+zx（z²-x²）
希望大家帮帮我把

Answer 1

1.原式=(x+3)(x+1)(x+5)(x+7)+15
=(x+1)(x+7)(x+3)(x+5)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=(x^2+8x+7+5)(x^2+8x+7+3)
=(x^2+8x+12)(x^2+8x+10)
=(x+2)(x+6)(x^2+8x+10)
2.原式=(a^2+19a)^2-408(a^2+19a)-124848
=(a^2+19a)^2-24*17(a^2+19a)-36*17*12*17
=(a^2+19a-36*17)(a^2+19a+12*17)
=(a-17)(a+36)(a^2+19a+204)
3.取ab=A,a+b=B
则原式=(A-1)^2+(B-2)(B-2A)
=A^2-2A+1+B^2-2AB-2B+4A
=A^2-2(B-1)A+B^2-2B+1
=A^2-2(B-1)A+(B-1)^2
=(A-B+1)^2
=(ab-a-b+1)^2
=(a-1)^2(b-1)^2
4.原式=yx^3-xy^3+zy^3-yz^3+xz^3-zx^3
=(y-z)x^3+(z-y)(z^2+y^2+zy)x+zy(y-z)(y+z)
=(y-z)(x^3-(z^2+y^2+yz)x+zy(y+z))
=(y-z)(x^3+(y+z)x^2-(y+z)x^2-(y^2+z^2+yz)x+yz(y+z))
=(y-z)(x^2(x+y+z)-(x+y+z)((y+z)x-zy))
=(y-z)(x+y+z)(x^2-(y+z)x+zy)
=(y-z)(x+y+z)(x-z)(x-y)
楼主还有什么不懂可以问我

Answer 2

4.xy（x²-y²）+yz（y²-z²）+zx（z²-x²）=yx^3-xy^3+zy^3-yz^3+xz^3-zx^3
=(y-z)x^3+(z-y)(z^2+y^2+zy)x+zy(y-z)(y+z)
=(y-z)(x^3-(z^2+y^2+yz)x+zy(y+z))
=(y-z)(x^3+(y+z)x^2-(y+z)x^2-(y^2+z^2+yz)x+yz(y+z))
=(y-z)(x^2(x+y+z)-(x+y+z)((y+z)x-zy))
=(y-z)(x+y+z)(x^2-(y+z)x+zy)
=(y-z)(x+y+z)(x-z)(x-y)