高中因式分解 求答案><

1.x^3－(2a－b)x^2－(2ab－a^2)x－2a^3
=x^3－2ax^2+bx^2－2abx+a^2x－2a^3
=x^2(x－2a)+bx(x－2a)+a^2(x－2a)
=(x^2+bx+a^2)(x－2a)

2.a^3+b^3+c^3+a^2(b+c)+b^2(c+a)+c^2(a+b)
=(a^3+b^2a+c^2a)+(b^3+a^2b+c^2b)+(c^3+a^2c+b^2c)
=a(a^2+b^2+c^2)+b(b^2+a^2+c^2)+c(c^2+a^2+b^2)
=(a+b+c)(a^2+b^2+c^2)

3.題目應為
x^3+(a+b+c)x^2+(ab+bc+ca)x+abc
=x^3+ax^2+bx^2+cx^2+abx+bcx+cax+abc
=(x^3+ax^2)+(bx^2+abx)+(cx^2+acx)+(bcx+abc)
=x^2(x+a)+bx(x+a)+cx(x+a)+bc(x+a)
=(x^2+bx+cx+bc)(x+a)
=(x+a)(x+b)(x+c)

4.x^4－x^3+2x^2－x+1
=(x^2+1)(x^2－x+1)

5.x^2y+xy^2+y^2z+yz^2+z^2y+z^2x+xz^2+3xyz
=(x^2y+xy^2+xyz)+(y^2z+yz^2+xyz)+(z^2x+xz^2+xyz)
=xy(x+y+z)+yz(y+z+x)+zx(x+z+y)
=(xy+yz+zx)(x+y+z)

6.(axy/2)－a^2y+axb/6－a^2b/3
=(1/6)(3axy－6a^2y+abx－2a^2b)
=(1/6)[(3axy－6a^2y)+(abx－2a^2b)]
=(1/6)[3ay(x－2a)+ab(x－2a)]
=(3ay+ab)(x－2a)/6

7.2x^4－4x^3+x^2+10x－15
=(2x^2－5)(x^2－2x+3)

8.x(y^2－z^2)－z(y^2－x^2)
=(xy^2－zy^2)+(zx^2－xz^2)
=y^2(x－z)+xz(x－z)
=(y^2+xz)(x－z)

9.x^2y^2－x^2－y^2－6xy+4
=(x^2y^2－4xy+4)-(x^2+2xy+y^2)
=(xy－2)^2－(x+y)^2
=(xy+x+y－2)(xy－x－y－2)

10.x^4+4x^3+10x^2+12x+9
=(x^2+2x+3)^2

I advice you not to ask so much questions at once.