百度云盘在线解压:分解因式题

做完了！

1.
(xy+1)(x+1)(y+1)+xy
=(xy+1)(xy+1+x+y)+xy
=(xy+1)²+(x+y)(xy+1)+xy
=(xy+1+x)(xy+1+y)

2.
(x³+y³)²-4xy[x^4+(xy)²+y^4-2xy(x²-xy+y²)]
=(x³+y³)²-4xy[(x^4+2x²y²+y^4)-x²y²-2xy(x²-xy+y²)]
=(x³+y³)²-4xy[(x²+y²)²-(xy)²-2xy(x²-xy+y²)]
=(x³+y³)²-4xy[(x²+y²+xy)(x²+y²-xy)-2xy(x²-xy+y²)]
=(x³+y³)²-4xy(x²+y²-xy)(x²+y²+xy-2xy)
=(x+y)²(x²+y²-xy)²-4xy(x²+y²-xy)²
=(x²+y²+2xy-4xy)(x²+y²-xy)²
=(x-y)²(x²+y²-xy)²

3.
x³(a+1)-xy(x-y)(a-b)+y³(b+1)
=x³(a+1)-xy(x-y)(a+1)+xy(x-y)(b+1)+y³(b+1)
=x(a+1)(x²-xy+y²)+y(b+1)(x²+y²-xy)
=(x²+y²-xy)[(a+1)x+(b+1)y]

4.
(ab+cd)(a²-b²+c²-d²)+(ac+bd)(a²+b²-c²-d²)
=(ab+cd)(a²-d²)-(ab+cd)(b²-c²)+(ac+bd)(a²-d²)+(ac+bd)(b²-c²)
=(ab+cd+ac+bd)(a²-d²)+(ac+bd-ab-cd)(b²-c²)
=(a+d)(b+c)(a+d)(a-d)+(a-d)(c-b)(b+c)(b-c)
=(a-d)(b+c)[(a+d)²-(b+c)²]
=(a-d)(b+c)(a+d+b+c)(a+d-b-c)

5.
xyz(x³+y³+z³)-x³y³-y³z³-z³x³
=x^4yz+xyz(y³+z³)-y³z³-x³(y³+z³)
=yz(x^4-y²z²)+x(yz-x²)(y³+z³)
=yz(x²+yz)(x²-yz)-x(x²-yz)(y³+z³)
=(x²-yz)(x²yz+y²z²-xy³-xz³)
=(x²-yz)[y²(z²-xy)-xz(z²-xy)]
=(x²-yz)(y²-xz)(z²-xy)

6. 已知x+y-z是复项式x^2+axy+by^2-5x+y+6的一个因式，求a、b的值并分解因式
x²+axy+by²-5x+y+6=(x-3)(x-2)+axy+y+by²。
根据十字相乘法，该式经因式分解后的形式应为(x+my-3)(x+ny-2)。
①m=1，z=3，此时对应展开式的系数得n=b,1+n=a,-2-3n=1，得n=-1，a=0，b=-1，
x²-y²-5x+y+6=(x+y-3)(x-y-2)
②n=1，z=2，此时对应展开式的系数得m=b,1+m=a,-3-2m=1，得m=-2，a=-1，b=-2，
x²-xy-2y²-5x+y+6=(x+y-2)(x-2y-3)

此类问题是你的作业吧？没有难度啊，为什么全拿出来了？这样不是很好啊......

遗憾，不能为这个赚分数。

就是上面的那个答案，这些题都比较简单，还是自己多动动脑筋吧！！！