几个数学因式分解的题

Question

1·、(x-y-z)(x-y+z)+(y-z+x)(y+z-x)
2、x^4+8x^2（x+1）+16(x+1)^2
3、4xy-3xz+8y-6z
4、(x+y)^2-4(x+y-1)
5、x^4+4
要有过程……谢谢……

Answer 1

1·、(x-y-z)(x-y+z)+(y-z+x)(y+z-x)
=（x-y-z)(x-y+z)-(x-y-z)(x+y-z)
=(x-y-z)(x-y+z-x-y+z)
=2(x-y-z)(z-y)

2、x^4+8x^2（x+1)+16(x+1)^2
=[x²+4(x+1)]²
=(x²+4x+4)²
=(x+2)⁴

3、4xy-3xz+8y-6z
=x(4y-3z)+2(4y-3z)
=(4y-3z)(x+2)

4、(x+y)^2-4(x+y-1)
=(x+y)²-4(x+y)+4
=(x+y-2)²

5、x^4+4
=x⁴+4x²+4-4x²
=(x²+2)²-4x²
=(x²+2x+2)(x²-2x+2)

Answer 2