神马作文网详细思路等,
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/14 13:33:14
详细思路等,
(1)原式=ac^3+bc^3-a^2c^2-abc^2-b^2c^2+a^2b^2
=(ac^3-a^2c^2)+(bc^3-abc^2)-(b^2c^2-a^2b^2)
=ac^2(c-a)+bc^2(c-a)-b^2(c+a)(c-a)
=(c-a)(ac^2+bc^2-b^2c-b^2a)
=(c-a)[bc(c-b)+a(c+b)(c-b)]
=(c-a)(c-b)(bc+ac+ab)
(2)令f(x)=(x-1)(x+1)(x+4)(x+6)-24
易知：f(-2)=0,f(-3)=0,f(0)=f(1)=f(-1)=-24
所以,设 f(x)=(x+2)(x+3)(ax^2+bx+c)
由f(1)=f(-1)=f(-4)=-24,
12(a+b+c)=-24
2(a-b+c)=-24
2(16a-4b+c)=-24
解得：a=1,b=5,c=-8
∴f(x)=(x+2)(x+3)(x^2+5x-8)
(3)原式=a3(b-c)+a(c^3-b^3)+bc(b^2-c^2)
=(b-c)[a^3-a(c^2+bc+b^2)+bc(b+c)]
=(b-c)[a(a^2-c^2)-bc(a-c)-b^2(a-c)]
=(a-c)(b-c)[a(a+c)-bc-b^2]
=(a-c)(b-c)[(a+b)(a-b)+c(a-b)]
=(a-b)(a-c)(b-c)(a+b+c)
=(ac^3-a^2c^2)+(bc^3-abc^2)-(b^2c^2-a^2b^2)
=ac^2(c-a)+bc^2(c-a)-b^2(c+a)(c-a)
=(c-a)(ac^2+bc^2-b^2c-b^2a)
=(c-a)[bc(c-b)+a(c+b)(c-b)]
=(c-a)(c-b)(bc+ac+ab)
(2)令f(x)=(x-1)(x+1)(x+4)(x+6)-24
易知：f(-2)=0,f(-3)=0,f(0)=f(1)=f(-1)=-24
所以,设 f(x)=(x+2)(x+3)(ax^2+bx+c)
由f(1)=f(-1)=f(-4)=-24,
12(a+b+c)=-24
2(a-b+c)=-24
2(16a-4b+c)=-24
解得：a=1,b=5,c=-8
∴f(x)=(x+2)(x+3)(x^2+5x-8)
(3)原式=a3(b-c)+a(c^3-b^3)+bc(b^2-c^2)
=(b-c)[a^3-a(c^2+bc+b^2)+bc(b+c)]
=(b-c)[a(a^2-c^2)-bc(a-c)-b^2(a-c)]
=(a-c)(b-c)[a(a+c)-bc-b^2]
=(a-c)(b-c)[(a+b)(a-b)+c(a-b)]
=(a-b)(a-c)(b-c)(a+b+c)