Question

求您回答我一些数学问题吧

11.分解因式：(1)（x+y)(x+y+2xy)+(xy+1)(xy-1)
(2)(x+y)(x+y+2xy)+(xy+1)(xy-1)
12.若a-b=2,a-c=1/2,求(b-c)^2-3(b-c)+9/4的值。
13.解方程：（x-2)(x+3)+(2-x)^2-(x-2)(2x-3)=20

Answer 1

(1)
(x+y)(x+y+2xy)+(xy+1)(xy-1)
=(x+y)^2+2xy(x+y)+(xy)^2-1
=(x+y+xy)^2-1^2
=(x+y+xy+1)(x+y+xy-1)
=[x(1+y)+(y+1)](x+y+xy-1)
=(x+1)(y+1)(x+y+xy-1)

(2)
一样

12.
a-b=2,a-c=1/2
相减(a-c)-(a-b)=1/2-2
b-c=-3/2
所以原式=(b-c-3/2)²=9

13.
(x-2)(x+3)+(2-x)²-(x-2)(2x-3)=20
(x-2)[(x+3)+(x-2)-(2x-3)]=20
4(x-2)=20
x-2=5
x=7