Question

(x+y+z)(x-y+z)-(y-x+z)(y-x-z)

(x+y+z)(x-y+z)-(y-x+z)(y-x-z)提公因式法，分解因式要有过程

Answer 1

(x+y+z)(x-y+z)-(y-x+z)(y-x-z)
=（x+z）^2 - y^2 - (y-x)^2 + z^2
=（x+z）^2 - (y-x)^2 + z^2 - y^2
= (x+z-y+x)(x+z+y-x) + (z-y)(z+y)
=(2x +z -y)(y+z) + (z-y)(z+y)
=(z+y)(2x+z-y+z-y)
=2(z+y)(x-y+z)

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追问

可以用提公因式法吗

追答

(x+y+z)(x-y+z)-(y-x+z)(y-x-z)
=（x+y+z)(x-y+z)+(y-x+z)(x-y+z)
=（x-y+z)(x+y+z+y-x+z)
=（x-y+z)(2y+2z)
=2（x-y+z)(y+z)

Answer 2

解：原式=（x+y+z)(x-y+z)+(y-x+z)(x-y+z)
=（x-y+z)(x+y+z+y-x+z)
=（x-y+z)(2y+2z)
=2（x-y+z)(y+z)

Answer 3

(x+y+z)(x-y+z)-(y-x+z)(y-x-z)
=(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)(y+z)