几个数学因式分解的题1·、(x-y-z)(x-y+z)+(y-z+x)(y+z-x)2、x^4+8x^2(x+1)+16
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几个数学因式分解的题
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
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
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)
=(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)
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