搜搜做题作业网就三道简单的因式分解题,
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就三道简单的因式分解题,
(1)x^3-(x^2)y-xy^2+y^3
(2)x^2-8xy+15y^2+2x-6y
(3)已知x^2+4x-1=0,求2x^4+8x^3-4x^2-8x+1的值.
（注：如x^3就是x的三次方）
(1)x^3-(x^2)y-xy^2+y^3
(2)x^2-8xy+15y^2+2x-6y
(3)已知x^2+4x-1=0,求2x^4+8x^3-4x^2-8x+1的值.
（注：如x^3就是x的三次方）
x^3-(x^2)y-xy^2+y^3
=x^3+y^2-xy(x+y)
=(x+y)(x^2-xy+y^2)-xy(x+y)
=(x+y)(x^2-xy+y^2-xy)
=(x+y)(x-y)^2
x^2-8xy+15y^2+2x-6y
=(x-5y)(x-3y)+2(x-3y)
=(x-3y)(x-5y+2)
x^2+4x-1=0
x^2+4x=1
2x^4+8x^3-4x^2-8x+1
=2x^2(x^2+4x)-4x^2-8x+1
=2x^2-4x^2-8x+1
=-2x^2-8x+1
=-2(x^2+4x)+1
=-2+1
= -1
=x^3+y^2-xy(x+y)
=(x+y)(x^2-xy+y^2)-xy(x+y)
=(x+y)(x^2-xy+y^2-xy)
=(x+y)(x-y)^2
x^2-8xy+15y^2+2x-6y
=(x-5y)(x-3y)+2(x-3y)
=(x-3y)(x-5y+2)
x^2+4x-1=0
x^2+4x=1
2x^4+8x^3-4x^2-8x+1
=2x^2(x^2+4x)-4x^2-8x+1
=2x^2-4x^2-8x+1
=-2x^2-8x+1
=-2(x^2+4x)+1
=-2+1
= -1