木材加工企业风险评估:关于初一因式分解

1.应该是8a^3-b^3-12a^2b+6ab^2
立方差+分组分解:
原式=(2a-b)(4a^2+2ab+b^2)-6ab(2a-b)
=(2a-b)(4a^2+2ab+b^2-6ab)
=(2a-b)(4a^2-4ab+b^2)
=(2a-b)(2a-b)^2
=(2a-b)^3
2.2x^2+4xy+2y^2-x-y-1
原式=2(x+y)^2-(x+y)-1
换元,令x+y=a
=2a^2-a-1
=(2a+1)(a-1)
∴原式=[2(x+y)+1][x+y-1]
=(2x+2y+1)(x+y-1)
3.可能是a^3+3a^2+3a+9
原式=a^2(a+3)+3(a+3)
=(a^2+3)(a+3)
或:
原式=a^3+3a^2+3a+1+8
=(a+1)^3+2^3
=(a+1+2)[(a+1)^2-2(a+1)+4]
=(a+3)(a^2+3)
4.x^4-x^3-7x^2+x+6
原式=x^3(x-1)-(7x^2-x-6)
=x^3(x-1)-(7x+6)(x-1)
=(x-1)(x^3-7x-6)
=(x-1)[x^3+x^2-(x^2+7x+6)]
=(x-1)[x^2(x+1)-(x+6)(x+1)]
=(x-1)(x+1)(x^2-x+6)
=(x-1)(x+1)(x-3)(x+2)
5.(a+b+c)^3-a^3-b^3-c^3
原式=[(a+b+c)^3-a^3]-(b^3+c^3)
=(a+b+c-a)[(a+b+c)^2+a(a+b+c)+a^2]-(b+c)(b^2-bc+c^2)
=(b+c)(3a^2+b^2+c^2+3ab+3ac+2bc)-(b+c)(b^2-bc+c^2)
=(b+c)(3a^2+3ab+3ac+3bc)
=3(b+c)(a^2+ab+ac+bc)
=3(b+c)[a(a+b)+c(a+b)]
=3(a+b)(a+c)(b+c)

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a^3-b^3-12a^2b+6ab^2
立方差+分组分解:
原式=(2a-b)(4a^2+2ab+b^2)-6ab(2a-b)
=(2a-b)(4a^2+2ab+b^2-6ab)
=(2a-b)(4a^2-4ab+b^2)
=(2a-b)(2a-b)^2
=(2a-b)^3
2.2x^2+4xy+2y^2-x-y-1
原式=2(x+y)^2-(x+y)-1
换元,令x+y=a
=2a^2-a-1
=(2a+1)(a-1)
∴原式=[2(x+y)+1][x+y-1]
=(2x+2y+1)(x+y-1)
3.可能是a^3+3a^2+3a+9
原式=a^2(a+3)+3(a+3)
=(a^2+3)(a+3)
或:
原式=a^3+3a^2+3a+1+8
=(a+1)^3+2^3
=(a+1+2)[(a+1)^2-2(a+1)+4]
=(a+3)(a^2+3)
4.x^4-x^3-7x^2+x+6
原式=x^3(x-1)-(7x^2-x-6)
=x^3(x-1)-(7x+6)(x-1)
=(x-1)(x^3-7x-6)
=(x-1)[x^3+x^2-(x^2+7x+6)]
=(x-1)[x^2(x+1)-(x+6)(x+1)]
=(x-1)(x+1)(x^2-x+6)
=(x-1)(x+1)(x-3)(x+2)
5.(a+b+c)^3-a^3-b^3-c^3
原式=[(a+b+c)^3-a^3]-(b^3+c^3)
=(a+b+c-a)[(a+b+c)^2+a(a+b+c)+a^2]-(b+c)(b^2-bc+c^2)
=(b+c)(3a^2+b^2+c^2+3ab+3ac+2bc)-(b+c)(b^2-bc+c^2)
=(b+c)(3a^2+3ab+3ac+3bc)
=3(b+c)(a^2+ab+ac+bc)
=3(b+c)[a(a+b)+c(a+b)]
=3(a+b)(a+c)(b+c)