高一 数学 因式分解（要有详细过程） 请详细解答,谢谢! (14 20:52:48)

1. 3x²+5xy--2y²+x+9y--4
=(3x-y)(x+2y)-(3x-y)+4x+8y-4
=(3x-y)(x+2y-1)+4(x+2y-1)
=(3x-y+4)(x+2y-1)

2. (x²+x+1)(x²+x+2)--12
=(x²+x)²+3(x²+x)+2-12
=(x²+x)²+3(x²+x)-10
=(x²+x+5)(x²+x-2)
=(x²+x+5)(x+2)(x-1)

3. (a+b--2ab)(a+b--2)+(1--ab)²
=(a+b)²-(2+2ab)(a+b)+4ab+1-2ab+a²b²
=(a+b)²-(2+2ab)(a+b)+1+2ab+a²b²
=(a+b)²-(2+2ab)(a+b)+(1+ab)²
=[(1+ab)-(a+b)]²
=(ab-a-b+1)²
=[a(b-1)-(b-1)]²
=(a-1)²(b-1)²

1.
由于3x2+5xy-2y2=(3x-y)(x+2y)，
故可设
3x2+5xy-2y2+x+9y-4
=(3x-y+a)(x+2y+b)
=3x2+5xy-2y2+(a+3b)x+(2a-b)y+ab.

由于3x2+5xy-2y2=(3x-y)(x+2y)，
故可设
3x2+5xy-2y2+x+9y-4
=(3x-y+a)(x+2y+b)
=3x2+5xy-2y2+(a+3b)x+(2a-b)y+ab.

比较两边系数最后解得a=4 b=1
∴原式=(3x-y+4)(x+2y-1).

2.
令a=x^2+x