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

问题描述:

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)
(2X-3Y)^3+(3X-2Y)^3-125(X-Y)^3
=(3X-2Y)^3-(5X-5Y)^3+(2X-3Y)^3
=(3X-2Y-5X+5Y)((3X-2Y)^2+(3X-2Y)(5X-5Y)+-(5X-5Y)^2]+(2X-3Y)^3
=(-2X+3Y)((3X-2Y)^2+(3X-2Y)(5X-5Y)+-(5X-5Y)^2]+(2X-3Y)^3
=(2X-3Y)((2X-3Y)^2-((3X-2Y)^2+(3X-2Y)(5X-5Y)+-(5X-5Y)^2]
后面括号里再自己化简一下,我写写比较麻烦。
(X^4-4X^2+1)(X^4+3X^2+1)+10X^4
=(x^4+1)^2-x^2(x^4+1)-12x^4+10x^4
=(x^4+1)^2-x^2(x^4+1)-2x^4
=(x^4+1+x^2)(x^4+1-2x^2)
=(x^2-1)^2(x^4+1+x^2)
数学式子不太会打,所以可能看起来比较吃力

(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-2...