Question

谁能帮我做一下这几道因式分解啊

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Answer 1

①9c^2(a+c)(a-c)-b(b+6c^2)
=9(ac)^2-9c^4-b^2-6bc^2
=(3ac)^2-(3c^2-b)^2
=(3ac+3c^2-b)(3ac-3c^2+b)
②x(x+1)(x-1)+xy(x-y)-y(y+1)(y-1)
=x^3-x+xy(x-y)-y^3+y
=(x-y)(x^2+xy+y^2)-(x-y)+xy(x-y)
=(x-y)(x^2+2xy+y^2-1)
=(x-y)(x+y+1)(x+y-1)
③(x+1)^4+(x^2-1)^2+(x-1)^4
设a=(x+1)^2,b=(x-1)^2
那么原式=a^2+ab+b^2=(a+b)^2-ab
=[2(x^2+1)]^2-(x^2-1)^2
={2(x^2+1)+(x^2-1)}{2(x^2+1)-(x^2-1)}
=(3x^2+1)(x^2+3)
④x^4+y^4+z^4+2(xy)^2+2(yz)^2+2(zx)^2
=(x^2+y^2)^2+2(x^2+y^2)z^2+z^4
=(x^2+y^2+z^2)^2
⑤x^4+3x^3+3x^2+4x+3
=x^2(x^2+3x+2)+(x^2+4x+3)
=x^2(x+1)(x+2)+(x+1)(x+3)
=(x+1)(x^3+2x^2+x+3)
⑥2x^4-x^3-6x^2-x+2
=x^3(2x-1)-(2x-1)(3x+2)
=(2x-1)(x^3-3x-2)
=(2x-1)[(x^3-x)-2(x+1)]
=(2x-1)(x+1)(x^2-x-2)
=(2x-1)(x+1)(x-2)(x+1)
=(2x-1)(x-2)(x+1)^2
⑦x^3-7x+6
=(x^3-x)-6(x-1)
=(x-1)(x^2+x-6)
=(x-1)(x+3)(x-2)

Answer 2

太多了，应分次提问。