Question

【分组分解法】（1）分解因式：x+y+ax+ay= （2）bx+by+ax+ay= （3）x ² -y ² +x+y=

（4）2a+4+3ab+6b= （5）a ² +2ab+b ² -1= （6）1-x ² -2xy-y ² =

Answer 1

x+y+ax+ay=（x+y)(a+1)
bx+by+ax+ay=(x+y)(a+b)
x ² -y ² +x+y=(x+y)(x-y+1)
2a+4+3ab+6b=2(a+2)+3b(a+2)=(3b+2)(a+2)
a ² +2ab+b ² -1=(a+b+1)(a+b-1)
1-x ² -2xy-y ²=(1-x-y)(1+x+y)

Answer 2

x+y+ax+ay
=(x+y)+a(x+y)
=(x+y)(a+1)
bx+by+ax+ay
=b(x+y)+a(x+y)
=(a+b)(x+y)
x ² -y ² +x+y
=(x+y)(x-y)+(x+y)
=(x+y)(x-y+1)
2a+4+3ab+6b
=2(a+2)+3b(a+2)
=(2+3b)(a+2)
a ² +2ab+b ² -1
=(a+b)²-1
=(a+b+1)(a+b-1)
1-x ² -2xy-y ²
=1-(x+y)²
=(1+x+y)(1-x-y)

Answer 3

（1）分解因式：x+y+ax+ay=x+y+a(x+y)=(x+y)(a+1)
（2）bx+by+ax+ay= b（x+y)+a(x+y)=（x+y)(a+b)
（3）x ² -y ² +x+y=(x+y)(x-y)+x+y=(x+y)(x-y+1)
（4）2a+4+3ab+6b= 2(a+2)+3b(a+2)=(a+2)(2+3b)
（5）a ² +2ab+b ² -1= (a+b)^2-1=(a+b+1)(a+b-1)
（6）1-x ² -2xy-y ² =1-(x^2+2xy+y^2)=1-(x+y)^2=(1+x+y)(1-x-y)