神马作文网一个数学的因式分解题和计算 (8 12:5:45)
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/13 23:48:19
一个数学的因式分解题和计算 (8 12:5:45)
1：y^2(x^2-2x)^3+y^2
2:(x-1)(x-2)(x-3)(x-4)
1：y^2(x^2-2x)^3+y^2
2:(x-1)(x-2)(x-3)(x-4)
(1)
y^2(x^2-2x)^3+y^2
=y^2[(x^2-2x)^3+1]
=y^2(x^2-2x+1)[(x^2-2x)^2-(x^2-2x)+1]
=y^2(x+1)^2(x^4-4x^3+3x^2+2x+1)
(2)
(x-1)(x-2)(x-3)(x-4)
=[(x-1)(x-4)][(x-2)(x-3)]
=(x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24
y^2(x^2-2x)^3+y^2
=y^2[(x^2-2x)^3+1]
=y^2(x^2-2x+1)[(x^2-2x)^2-(x^2-2x)+1]
=y^2(x+1)^2(x^4-4x^3+3x^2+2x+1)
(2)
(x-1)(x-2)(x-3)(x-4)
=[(x-1)(x-4)][(x-2)(x-3)]
=(x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24