Question

高分悬赏，因式分解在线等

1、 x(x+1)(x+2)(x+3)+1
2、 x^2+3xy+2y^2+2x+4y
3、 (x^2-1)(x+3)(x+5)+12
4 、 (x+y-2xy)(x+y-2)+(xy-1)^2
5 、 x^2-6xy+9y^2-5xy+15yz+6z^2
6、 (x+2)(x+3)(x+4)(x+6)-42x^2

Answer 1

答：
1.原式
=[x(x+3)][(x+1)(x+2)]+1
=(x^2+3x)(x^2+3x+2)+1
=(x^2+3x)^2+2(x^2+3x)+1
=(x^2+3x+1)^2

2原式
=(x^2+3xy+2y^2)+(2x+4y)
=(x+2y)(x+y)+2(x+2y)
=(x+2y)(x+y+2)

3.原式
=(x+1)(x-1)(x+3)(x+5)+12
=[(x+1)(x+3)][(x-1)(x+5)]+12
=(x^2+4x+3)(x^2+4x-5)+12
=(x^2+4x)^2-2(x^2+4x)-15+12
=(x^2+4x)^2-2(x^2+4x)-3
=(x^2+4x-3)(x^2+4x+1)

4.原式
=(x+y)^2-2(x+y)-2xy(x+y)+4xy+x^2y^2-2xy+1
=[(x+y)^2-2xy(x+y)+x^2y^2]-2(x+y)+2xy+1
=(x+y-xy)^2-2(x+y-xy)+1
=(x+y-xy-1)^2
=[(x-1)(1-y)]^2
=(x-1)^2(y-1)^2

5.
那个-5xy应该是-5xz吧?

6.原式
=[(x+2)(x+6)][(x+3)(x+4)]-42x^2
=(x^2+12+8x)(x^2+12+7x)-42x^2
=(x^2+12)^2+(8x+7x)(x^2+12)+56x^2-42x^2
=(x^2+12)^2+15x(x^2+12)+14x^2
=(x^2+12+14x)(x^2+12+x)
=(x^2+14x+12)(x^2+x+12)

Answer 2

1、 x(x+1)(x+2)(x+3)+1
=[x(x+3)][(x+1)(x+2)]+1
=(x^2+3x)(x^2+3x+2)+1
=(x^2+3x)^2+2(x^2+3x)+1
=(x^2+3x+1)^2

2、 x^2+3xy+2y^2+2x+4y
= (x^2+3xy+2y^2)+(2x+4y)
=(x+2y)(x+y)+2(x+2y)
=(x+2y)(x+y+2)

3、 (x^2-1)(x+3)(x+5)+12
=(x+1)(x-1)(x+3)(x+5)+12
=[(x+1)(x+3)][(x-1)(x+5)]+12
=(x^2+4x+3)(x^2+4x-5)+12
=(x^2+4x)^2-2(x^2+4x)-15+12
=(x^2+4x)^2-2(x^2+4x)-3
=(x^2+4x-3)(x^2+4x+1)

4 、 (x+y-2xy)(x+y-2)+(xy-1)^2
=(x+y)^2-2(x+y)-2xy(x+y)+4xy+x^2y^2-2xy+1
=[(x+y)^2-2xy(x+y)+x^2y^2]-2(x+y)+2xy+1
=[(x+y)^2-2xy(x+y)+x^2y^2]-2[(x+y)-xy]+1
=(x+y-xy)^2-2(x+y-xy)+1
=(x+y-xy-1)^2
=[(x-1)(1-y)]^2
=(x-1)^2(y-1)^2

5 、 x^2-6xy+9y^2-5xy+15yz+6z^2
=-6xy???-5xy???