简单的数学题1.因式分解：ab(
1、ab(a-b)+bc(b-c)+ca(c-a)=a^2b-ab^2+bc(b-c)+c^2a-ca^2=a^2(b-c)+bc(b-c)-a(b^2-c^2)=(b-c)(a^2+bc-ab-ac)=(b-c)[(a^2-ab)-(ac-bc)]=(b-c)[a(a-b)-c(a-b)]=(b-c)(a-b)(a-c)
2、a^2(b-c)+b^2(c-a)+c^2(a-b)=a^2b-a^c+b^2c-b^2a+c^2(a-b)=a^2b-b^2a-a^c+b^2c+c^2(a-b)=ab(a-b)-c(a^2-b^2)+c^2(a-b)=(a-b)(ab-ac-bc+c^2)=(a...全部
1、ab(a-b)+bc(b-c)+ca(c-a)=a^2b-ab^2+bc(b-c)+c^2a-ca^2=a^2(b-c)+bc(b-c)-a(b^2-c^2)=(b-c)(a^2+bc-ab-ac)=(b-c)[(a^2-ab)-(ac-bc)]=(b-c)[a(a-b)-c(a-b)]=(b-c)(a-b)(a-c)
2、a^2(b-c)+b^2(c-a)+c^2(a-b)=a^2b-a^c+b^2c-b^2a+c^2(a-b)=a^2b-b^2a-a^c+b^2c+c^2(a-b)=ab(a-b)-c(a^2-b^2)+c^2(a-b)=(a-b)(ab-ac-bc+c^2)=(a-b)[(ab-ac)-(bc-c^2)]=(a-b)[(ab-ac)-(bc-c^2)]=(a-b)[a(b-c)-c(b-c)]=(a-b)(b-c)(a-c)
3、x^4+4a^4=(x^2)^2+(2a^2)^2+2a^2x^2-2a^2x^2=(x^2+2a^2)^2-(√2ax)^2
=(x^2+√2ax+2a^2)(x^2-√2ax+2a^2)
4、x^3-7x-6=x^3-x-6x-6=x(x^2-1)-6(x-1)=(x-1)(x^2+x-6)=(x-1)(x-2)(x+3)
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