Question

12道十字相乘因式分解题

1. x²-xy-2y²
2. x²+6xy+8y²
3. 2x²-xy-y²
4. 4x²-xy-5y²
5. abcx²+(a²b²+c²)x+abc
6. mnx²-(m²+n²)xy+mny²
7. (x²-2) ²-(x²-2)-2
8. (x²+4x) ²-x²-4x-20
9. (x+y)(x+y+2xy)+x²y²-1
10. x²-3xy-10y²+x+9y-2
11. a²+ab-6b²+5a+35b-36
12. x³-3x²+4
15分钟内答，加15分，详细，加20分。谁能在后面给我把什么是双十字相乘法讲清楚，再加20分。最高共能得80分。不想要只有答案的那种，想要一下过程。如果我发现回答的非常详细，还会加分哦！

Answer 1

1. x²-xy-2y²=(x+y)(x-2y)
2. x²+6xy+8y²=(x+2y)(x+4y)
3. 2x²-xy-y²=(2x+y)(x-y)
4. 4x²-xy-5y²=(4x-5y)(x+y)
5. abcx²+(a²b²+c²)x+abc=(abx+c)(cx+ab)
6. mnx²-(m²+n²)xy+mny²=(mx-ny)(nx-my)
7. (x²-2) ²-(x²-2)-2=[(x²-2)+1][(x²-2)-2]=(x²-1)(x²-4)=(x+1)(x-1)(x+2)(x-2)
8. (x²+4x) ²-x²-4x-20=(x²+4x)²-(x²+4x)-20=[(x²+4x)+4][(x²+4x)-5]=(x+2)²(x-1)(x+5)
9. (x+y)(x+y+2xy)+x²y²-1=(x+y)²+2xy(x+y)+(xy)²-1=(x+y+xy)²-1=(x+y+xy+1)(x+y+xy-1)
=(x+1)(y+1)(x+y+xy-1)
10. x²-3xy-10y²+x+9y-2=(x²-3xy-10y²)+x+9y-2=(x+2y)(x-5y)+2(x+2y)-(x-5y)-2
=(x+2y-1)(x-5y+2)
11. a²+ab-6b²+5a+35b-36=(a²+ab-6b²)+5a+35b-36=(a-2b)(a+3b)-4(a-2b)+9(a+3b)-36
=(a-2b+9)(a+3b-4)
12. x³-3x²+4=(x³+x²)-(4x²-4)=x²(x+1)-4(x+1)(x-1)=(x+1)(x²-4x+4)=(x+1)(x-2)²
具体的十字相乘的方法可以参考百度百科啊……http://baike.baidu.com/view/198055.htm

Answer 2

现在答 行不行