Question

帮忙做几题因式分解，谢谢： 1.a^2-b^2+4a+2b+3 2.x^2-2x-2y^2+4y-xy 3.x(x-1)+y(y+1)-2xy

1.a^2-b^2+4a+2b+3
2.x^2-2x-2y^2+4y-xy
3.x(x-1)+y(y+1)-2xy

Answer 1

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

x^2-2x-2y^2+4y-xy
=(x^2-xy-2y^2)-(2x-4y)
=(x-2y)(x+y)-2(x-2y)
=(x-2y)(x+y-2)

x(x-1)+y(y+1)-2xy
=x^2-x+y^2+y-2xy
=x^2+y^2-2xy-(x-y)
=(x-y)^2-(x-y)
=(x-y)(x-y-1)

Answer 2

【1】
a²-b²+4a+2b+3
=(a²+4a+4)-(b²-2b+1)
=(a+2)²-(b-1)²
=[(a+2)+(b-1)][(a+2)-(b-1)]
=(a+b+1)(a-b+3)
【2】
x²-2x-2y²+4y-xy
=(x²-xy-2y²)-(2x-4y)
=(x-2y)(x+y)-2(x-2y)
=(x-2y)(x+y-2)
【3】
x(x-1)+y(y+1)-2xy
=(x²-2xy+y²)-(x-y)
=(x-y)²-(x-y)
=(x-y)(x-y-1)

Answer 3

1. a^2-b^2+4a+2b+3
=a²+4a+4-b²+2b-1
=(a+2)²-(b-1)²
=(a+2+b-1)(a+2-b+1)
=(a+b+1)(a-b+3)

2 .x^2-2x-2y^2+4y-xy
=x²-xy-2y²-2x+4y
=(x-2y)(x+y)-2(x-2y)
=(x-2y)(x+y-2)

3. x(x-1)+y(y+1)-2xy
=x²-x+y²+y-2xy
=(x-y)²-(x-y)
=(x-y)(x-y-1)

Answer 4

a^2-b^2+4a+2b+3=a2+4a+4-b2+2b-1=(a+2)2-(b-1)2