Question

分解因式的题~帮帮忙吧~

(1) x^2+7x-18
(2) y^2+7y+10
(3) x^2-2x-8
(4) (a+b+c)^2-(a-b-c)^2
(5) 已知x^2+y^2+2x-6y+10=0,求x+y的值

（注意标清序号。。）
帮帮忙~谢谢啦~

Answer 1

(1) x^2+7x-18
=(x-2)(x+9)
(2) y^2+7y+10
=(x+2)(x+5)
(3) x^2-2x-8
=(x+2)(x-4)
(4) (a+b+c)^2-(a-b-c)^2
=(a+b+c+a-b-c)(a+b+c-a+b+c)
=2a(2b+2c)
=4a(b+c)
(5) 已知x^2+y^2+2x-6y+10=0,求x+y的值
(x+1)²+(y-3)²=0
x+1=0,y-3=0
x=-1,y=3
x+y=-1+3=2

追问

前三道题是用十字相乘法是吧。。

追答

是的！

Answer 2

(1) x^2+7x-18 = (x+9)(x-2)
(2) y^2+7y+10 =(y+2)(y+5)
(3) x^2-2x-8 = (x-4)(x+2)
(4) (a+b+c)^2-(a-b-c)^2 = (a+b+c+(a-b-c))(a+b+c-(a-b-c)) = 4a(b+c)
(5) 已知x^2+y^2+2x-6y+10=0,求x+y的值
x^2+y^2+2x-6y+10=0
(x+1)^2+(y-3)^2=0
x+1=0 and (y-3)=0
x+y = -1+3 = 2