在线等。初二，因式分解。

来源：百度知道 编辑：UC知道 时间：2024/05/23 15:02:00
分解下列因式

① x2-y2+ax+ay ② x2+x-y2-y ③2ac+3bc+6a+9b

④ 2ab-a2-b2+1 ⑤ x2+xy-3x-3y ⑥x2-x-4y2+2y

⑦ a2-c2+b2-2ab-2c-1 ⑧ x2-y2-x+¼ ⑨ ab-a-b+1

⑩x2-2xy-9+y2

注：X2=X的平方、
X3=X的立方
用分组分解法。！！

① x2-y2+ax+ay
=(x+y)(x-y)+a(x+y)
=(x+y)(x-y+a)
② x2+x-y2-y
=(x+y)(x-y)+(x-y)
=(x-y)(x+y+1)
③2ac+3bc+6a+9b
=c(2a+3b)+3(2a+3b)
=(c+3)(2a+3b)
④ 2ab-a2-b2+1
=1-(a-b)^2
=(1-a+b)(1+a-b)
⑤ x2+xy-3x-3y
=x(x-3)+y(x-3)
=(x+y(x-3)

⑥x2-x-4y2+2y
=(x-2y)(x+2y)-(x-2y)
=(x-2y)(x+2y-1)

⑦ a2-c2+b2-2ab-2c-1
=(a-b)^2-(c+1)^2
=(a-b-c-1)(a-b+c+1)
⑧ x2-y2-x+¼
=(x-1/2)^2-y^2
=(x-1/2-y)(x-1/2+y)
⑨ ab-a-b+1
=a(b-1)-(b-1)
=(a-1)(b-1)
⑩x2-2xy-9+y2
=(x-y)^2-9
=(x-y-3)(x-y+3)

①(x-a/2)^2-(y-a/2)^2 都是配方