请问这几个题如何因式分解x^2y＋x^2z-xy^2-y^2z3a^2-2b^2+5ab-2a+3b-1x^2-y^2+4y-4ab(a+b)+bc(b+c)+ca(c+a)+2abc

Question

请问这几个题如何因式分解
x^2y＋x^2z-xy^2-y^2z
3a^2-2b^2+5ab-2a+3b-1
x^2-y^2+4y-4
ab(a+b)+bc(b+c)+ca(c+a)+2abc

Answer 1

1.x^2y＋x^2z-xy^2-y^2z=(x^2y-xy^2)+(x^2z-y^2z)=xy(x-y)+z(x-y)(x+y)
=(x-y)(xy+xz+yz)
2.3a^2-2b^2+5ab-2a+3b-1=(a+2b-1)(3a-b+1)
3.x^2-y^2+4y-4=x^2-(y^2-4y+4)=x^2-(y-2)^2=(x-y+2)(x+y-2)
4.ab(a+b)+bc(b+c)+ca(c+a)+2abc
=a^2b+ab^2+a^2c+ac^2+b^2c+bc^2+2abc
=(a^2b+bc^2+2abc )+(ab^2+b^2c) +(a^2c+ac^2)
=b(a+c)^2+b^2(a+c)+ac(a+c)=(a+c)(b^2+ab+bc+ac)
=(a+c)(a+b)(b+c)