4道数学因式分解题求解

Question

如题所述

Answer 1

①6x^4+7x^3-36x^2-7x+6
=6(x^2-1)^2+7x(x^2-1)-24x^2
=[3(x^2-1)+8x][2(x^2-1)-3x]
=(3x^2+8x-3)(2x^2-3x-2)
=(3x-1)(x+3)(2x+1)(x-2)
②a^2*b-ab^2+a^2*c-ac^2-3abc+b^2*c+bc^2
=(a^2*b-ab^2-abc)+(a^2*c-ac^2-abc)+(b^2*c+bc^2-abc)
=ab(a-b-c)+ac(a-c-b)+bc(b+c-a)
=(a-b-c)(ab+ac-bc)
③x^3*(a+1)-xy(x-y)(a-b)+y^3*(b+1)
解 设m=a+1,n=b+1
原式=mx^3-xy(x-y)(m-n)+ny^3
=mx^3-mxy(x-y)+nxy(x-y)+ny^3
=mx(x^2-xy+y^2)+ny(x^2-xy+y^2)
=(x^2-xy+y^2)(mx+ny)
=(x^2-xy+y^2)[(a+1)x+(b+1)y]
④2x^3-4x^2*y-x^2*z+2xy^2+2xyz-y^2*z
=2x(x^2-2xy+y^2)-z(x^2-2xy+y^2)
=(2x-z)(x^2-2xy+y^2)
=(2x-z)(x-y)^2

Answer 2

第一题是3x的四次方减二