分解因式:（x^2+1）^2-4x(x^2+1)+4x^2

1（x^2+1）^2-4x(x^2+1)+4x^2
=（x^2+1）^2-2*2x(x^2+1)+(2x)^2
=(x^2+1-2x)^2
=(x-1)^4

2a^2+4a+b^2-2ab-4b+3
=a^2b^2-2ab+4a-4b+3
=(a-b)^2+4(a-b)+3
=(a-b+1)(a-b-3)

3 x^2-9y^2+2x-6y
=(x^2-9y^2)+(2x-6y)
=(x+3y)(x-3y)+2(x-3y)
=(x+3y+2)(x-3y)

4 (x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y)^2-2*2*(x+y)+2^2
=(x+y-2)^2

大同小异哈

1. 把x^2+1看做一项a,2x看做另一项b.
=(a-b)^2=(x^2-2x+1)^2=(x-1)^4
2. 把a-b看做x,=x^2+4x+3=(x+1)(x+3)=(a-b+1)(a-b+3)
3. =[(x+1)^2-1]-[(3y+1)^2-1]=(x+1)^2-(3y+1)^2
下面就用平方差了,最后=(x+3y+2)(x-3y)
4. =(x+y)^2-4(x+y)+4
看出来了吧.=(x+y-2)^2

分解因式：x+4x-1

1、（x^2+1）^2-4x(x^2+1)+4x^2
=(x^2+1-2x)^2=(x-1)^4
2、a^2+4a+b^2-2ab-4b+3
=(a-b)^2+4(a-b)+3
=(a-b+1)(a-b+3)
3、x^2-9y^2+2x-6y
=(x+3y)*(x-3y)+2(x-3y)
=(x+3y+2)(x-3y)
4、(x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y-2)^2

（x^2+1）^2-4x(x^2+1)+4x^2
=（x^2+1）^2-2*2x(x^2+1)+(2x)^2
=(x^2+1-2x)^2
=(x-1)^4

a^2+4a+b^2-2ab-4b+3
=a^2b^2-2ab+4a-4b+3
=(a-b)^2+4(a-b)+3
=(a-b+1)(a-b-3)

x^2-9y^2+2x-6y
=(x^2-9y^2)+(2x-6y)
=(x+3y)(x-3y)+2(x-3y)
=(x+3y+2)(x-3y)

(x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y)^2-2*2*(x+y)+2^2
=(x+y-2)^2