因式分解ab(x的二次方+1)+x(a的二次方+b的二次方)还有几道题、顺便了吧、谢谢4a^2-ab+b^2-c^29m^2-6m+2n-n^2（z^2-x^2-y^2）^2-4x^2y^25x^3-15x^2-x+3

Question

因式分解ab(x的二次方+1)+x(a的二次方+b的二次方)
还有几道题、顺便了吧、谢谢
4a^2-ab+b^2-c^2
9m^2-6m+2n-n^2
（z^2-x^2-y^2）^2-4x^2y^2
5x^3-15x^2-x+3

Answer 1

1,ab(x^2+1)+x(a^2+b^2)=abx^2+x(a^2+b^2)+ab
=(ax+b)(bx+a)
2,4a^2-ab+b^2-c^2(题有误)
3,9m^2-6m+2n-n^2
=(3m-1)^2-(n-1)^2=(3m+n-2)(3m-n)
4,（z^2-x^2-y^2）^2-4x^2y^2
=(z^2-x^2-y^2+2xy)(z^2-x^2-y^2-2xy)
=(z+x-y)(z-x+y)(z+x+y)(z-x-y)
5,5x^3-15x^2-x+3
=5x^2(x-3)-(x-3)
=(x-3)(5x^2-1)
或
=(x-3)(5x^2-1)=(x-3)(√5x+1)(√5x-1)