UC知道分解因式题
来源：百度知道 编辑：UC知道 时间：2024/05/11 14:59:08
1. (xy+1)(x+1)(y+1)+xy
2. ( x^3+y^3)^2-4xy[x^4+(xy) ^2+y^4-2xy(x^2-xy+y^2)]
3. x^3 (a+1)-xy(x-y)(a-b)+y^3(b+1)
4. (ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-c^2-d^2)
5. xyz(x^3+y^3+z^3)-(xy) ^3-(yz) ^3-(zx) ^3
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
2. ( x^3+y^3)^2-4xy[x^4+(xy) ^2+y^4-2xy(x^2-xy+y^2)]
3. x^3 (a+1)-xy(x-y)(a-b)+y^3(b+1)
4. (ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-c^2-d^2)
5. xyz(x^3+y^3+z^3)-(xy) ^3-(yz) ^3-(zx) ^3
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
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.