学帮网分组分解法分解因式题目4a^2+4a-4a^2b+b+14x^4+1x^4-7x^2+1（1-x^2)(1-y^2）-4xyx(x-2)-y^2+1x^4-xy^3-x^3y-3x^2y+3xy^3+y^4
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/08 18:39:34
分组分解法分解因式题目
4a^2+4a-4a^2b+b+1
4x^4+1
x^4-7x^2+1
（1-x^2)(1-y^2）-4xy
x(x-2)-y^2+1
x^4-xy^3-x^3y-3x^2y+3xy^3+y^4
1.=(4a^2+4a+1)-b(4a^2-1) *
=(2a+1)^2-b(2a+1)(2a-1)
=(2a+1)[2a+1-b(2a-1)]
=(2a+1)(-2ab+2a+b+1)
=-(2a+1)(2ab-2a-b-1)
2.=(4x^4+4x^2+1)-4x^2 *
=(2x^2+1)^2-(2x)^2
=(2x^2+2x+1)(2x^2-2x+1)
3.=(x^4+2x^2+1)-9x^2 *
=(x^2+1)^2-(3x)^2
=(x^2+3x+1)(x^2-3x+1)
4.=x^2y^2-x^2-y^2-4xy+1
=(x^2y^2-2xy+1)-(x^2+2xy+y^2) *
=(xy-1)^2-(x+y)^2
=(xy+x+y-1)(xy-x-y-1)
5.=x^2-2x-y^2+1
=(x^2-2x+1)-y^2 *
=(x-1)^2-y^2
=(x+y-1)(x-y-1)
4a^2+4a-4a^2b+b+1
=4a^2+4a+1-b(4a^2-1)
=(2a+1)^2-b(2a+1)(2a-1)
=(2a+1)*[2a+1-b(2a-1)]
=(2a+1)*(2a-2ab+b+1)
4x^4+1
=4x^4+4x^2+1-4x^2
=(2x^2+1)^2-(2x)^2
=(2x^2-2x+1)(2x^2...
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4a^2+4a-4a^2b+b+1
=4a^2+4a+1-b(4a^2-1)
=(2a+1)^2-b(2a+1)(2a-1)
=(2a+1)*[2a+1-b(2a-1)]
=(2a+1)*(2a-2ab+b+1)
4x^4+1
=4x^4+4x^2+1-4x^2
=(2x^2+1)^2-(2x)^2
=(2x^2-2x+1)(2x^2+2x+1)
x^4-7x^2+1
=x^4+2x^2+1-9x^2
=(x^2+1)^2-(3x)^2
=(x^2-3x+1)(x^2+3x+1).
(1-x^2)(1-y^2)-4xy
=1 - x^2 - y^2 + x^2 * y^2 - 4xy
=(1-2xy+x^2 * y^2 )-(x^2+2xy+y^2 )
=(1-xy)^2 -(x+y)^2
=(1-xy+x+y)(1-xy-x-y )
x(x-2)-y^2+1
=x^2-2x+1-y^2
=(x-1)^2-y^2
=(x-1+y)(x-1-y)
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(2a+1)(2a+1+2ab-b)
(2x^2+1+2x)(2x^2+1-2x)
(x^2+根号5乘以x-1)（x^2-根号5乘以x-1）
(xy-1+x+y)(xy-1-x-y)
(x-1-y)(x-1+y)