UC知道分解因式～～～
来源：百度知道 编辑：UC知道 时间：2024/05/18 01:53:32
(1)(x+y)a+(y+z)a+(z+x)a
(2)a^3(b+c-d)+a^2b(c+d-a)-a^2c(d+a+b)注意：＾是根号的意思！比如a^3就是说a的三次方，a^2就是a的二次方
(3)(a+b)^2*(x-2y)+(b-a)^2*(2x-y)
(4)(a-b)^4+a(a-b)^3+b(b-a)^3
(2)a^3(b+c-d)+a^2b(c+d-a)-a^2c(d+a+b)注意：＾是根号的意思！比如a^3就是说a的三次方，a^2就是a的二次方
(3)(a+b)^2*(x-2y)+(b-a)^2*(2x-y)
(4)(a-b)^4+a(a-b)^3+b(b-a)^3
(1)(x+y)a+(y+z)a+(z+x)a
=a(x+y+y+z+z+x)
=2a(x+y+z)
(2)a^3(b+c-d)+a^2b(c+d-a)-a^2c(d+a+b)
=a^2(ab+ac-ad+bc+bd-ab-cd-ac-bc)
=a^2(bd-ad-cd)
=da^2(b-a-c)
(3)(a+b)^2*(x-2y)+(b-a)^2*(2x-y)
=(a^2+b^2+2ab)*(x-2y)+(a^2+b^2-2ab)*(2x-y)
=(a^2+b^2)*(x-2y)+2ab*(x-2y)+(a^2+b^2)*(2x-y)-2ab*(2x-y)
=(a^2+b^2)*(x-2y+2x-y)+2ab*(x-2y-2x+y)
=3(a^2+b^2)*(x-y)-6ab*(x-y)
=3(a^2+b^2-2ab)*(x-y)
=3(a-b)^2*(x-y)
(4)(a-b)^4+a(a-b)^3+b(b-a)^3
=(a-b)^3(a-b+a-b)
=0