神马品牌网耐克cr7足球鞋:分解因式
来源：百度文库 编辑：神马品牌网 时间：2024/05/06 09:25:00
(1+y)ˇ2-2xˇ2(1+y2)+xˇ4(1-9)ˇ2
xˇ2是x的平方
xˇ2是x的平方
是不是:
(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
=x^4y^2-2x^2y^2+y^2+x^4-2x^2+1-2x^4y+2y
=y^2(x^4-2x^2+1)+(x^4-2x^2+1)-2y(x^4-1)
=y^2(x+1)^2(x-1)^2+(x+1)^2(x-1)^2-2y(x^2+1)(x+1)(x-1)
=(x+1)(x-1)[y^2(x+1)(x-1)+(x+1)(x-1)-2y(x^2+1)]
=(x+1)(x-1)(x^2y^2-2x^2y+x^2-y^2-2y-1)
=(x+1)(x-1)[x^2(y-1)^2-(y+1)^2]
=(x+1)(x-1)(xy-x+y+1)(xy-x-y-1)
a^2-4ab+4b^2-c^2
=(a-2b)^2-c^2
=(a-2b+c)(a-2b-c)
是不是:
(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
=x^4y^2-2x^2y^2+y^2+x^4-2x^2+1-2x^4y+2y
=y^2(x^4-2x^2+1)+(x^4-2x^2+1)-2y(x^4-1)
=y^2(x+1)^2(x-1)^2+(x+1)^2(x-1)^2-2y(x^2+1)(x+1)(x-1)
=(x+1)(x-1)[y^2(x+1)(x-1)+(x+1)(x-1)-2y(x^2+1)]
=(x+1)(x-1)(x^2y^2-2x^2y+x^2-y^2-2y-1)
=(x+1)(x-1)[x^2(y-1)^2-(y+1)^2]
=(x+1)(x-1)(xy-x+y+1)(xy-x-y-1)