Question

因式分解 指定要用配方法 要有过程

(a-4)b+(4-a)c

a^2c-abd-abc+a^2d

(a+2b)^3-(a-2b)^3

x^4-x^3+x-1

x^3-ax^2-b^2x+ab^2

Answer 1

(a-4)b+(4-a)c
=(a-4)b-(a-4)c
=(a-4)(b-c)

a^2c-abd-abc+a^2d
=a{ac-bd-bc+ad}
=a{ac-bc+ad-bd}
=a{c(a-b)+d(a-b)}
=a(a-b)(c+d)

(a+2b)^3-(a-2b)^3
={(a+2b)-(a-2b)}{(a+2b)^2+(a+2b)(a-2b)+(a-2b)^2}
=4b{a^2+4b^2+a^2-4b^2+a^2+4b^2}
=4b(3a^2+4b^2)

x^4-x^3+x-1
=x^3(x-1)+(x-1)
=(x-1)(x^3+1)
=(x-1)(x+1)(x^2-x+1)

x^3-ax^2-b^2x+ab^2
=x^2(x-a)-b^2(x-a)
=(x-a)(x^2-b^2)
=(x-a)(x+b)(x-b)