几道初中因式分解(XY)^2+2XY+1-(X+Y)^2(2X-3Y)^3+(3X-2Y)^3-125(X-Y)^3(X

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/17 02:37:26

几道初中因式分解
(XY)^2+2XY+1-(X+Y)^2
(2X-3Y)^3+(3X-2Y)^3-125(X-Y)^3
(X^4-4X^2+1)(X^4+3X^2+1)+10X^4

(XY)^2+2XY+1-(X+Y)^2
=(xy+1)^2-(x+y)^2
=(xy+1-x-y)(xy+1+x+y)
(X^4-4X^2+1)(X^4+3X^2+1)+10X^4
=(X^4+1)^2-x^2(x^4+1)-2x^4
=(x^4+1-2x^2)(X^4+1+x^2)
=(x^2-1)^2（x^2+1）^2
=(x+1)^2(x-1)^2(x^2+1)^2
(2x-3y)^3+(3x-2y)^3-125(x-y)^3
= (2x-3y)^3+(3x-2y)^3-(5x-5y)^3
= (2x-3y)^3+(3x-2y)^3-((2x-3y) +(3x-2y))^3
令m =2x-3y,n =3x-2y
原式
= m^3 +n^3 -(m+n)^3
= m^3 +n^3 -(m^3 +n^3 +3mn^2 +3m^2n)
= -3mn^2 -3m^2n
= -3mn(m+n) .(将假设带入）
= -3(2x-3y)(3x-2y)((2x-3y)+(3x-2y))
= -3(2x-3y)(3x-2y)(5x-5y)
= -15(2x-3y)(3x-2y)(x-y)

几道初中因式分解(XY)^2+2XY+1-(X+Y)^2(2X-3Y)^3+(3X-2Y)^3-125(X-Y)^3(X 因式分解x^3+x^2y-xy^2-y^3 x^3-x^2y-xy^2+y^3因式分解因式分解x^3+x^2y-xy^2+y^3 x^2y+3xy^2-x-3y因式分解 -x^3y^3-x^2y^2-xy 因式分解. 因式分解 x^2-2xy-3y^2+x+y x^2+x^2y-xy^2-y^3因式分解 x^3-x^2y-xy^2+y因式分解把2x-2y+3xy(x-y)因式分解 y^3+xy^2+2xy+x^2-1 因式分解因式分解(x+y)^3+2xy(1-xx-y)-1