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

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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

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
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

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)

(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-3...

全部展开

(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

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