1)(a+b-c)^2

=(a+b)^2-2(a+b)c+c^2

=a^2+2ab+b^2-2ac-2bc+c^2

=a^2+b^2+c^2+2ab-2ac-2bc

2)(x+y/2)^2+(x-y/2)^2

=x^2+xy+y^2/4+x^2-xy+y^2/4

=2x^2+ 1/2*y^2

3)(a+b)^2

=a^2+2ab+b^2

=a^2-2ab+b^2+4ab

=(a-b)^2+4ab

=2^2+4* 1

=8

4)(a+2b+3c)*(a+2b-3c)

=(a+2b)^2-(3c)^2

=a^2+4ab+4b^2-9c^2

5)(x-2y)*(x+2y)-(x+2y)？ +8y？

=(x+2y)(x-2y-x-2y)+8y^2

=-4y(x+2y)+8y^2

=-4xy-8y^2+8y^2

=-4xy

6)(x+y-z)

= x 2+y 2+z 2+2xy-2xz-2yz Please refer to the question 1) for specific steps, but the letters are different and the process is the same.

7)(x-y+2z)^2

=(x-y)^2+4z(x-y)+4z^2

=x^2-2xy+y^2+4xz-4yz+4z^2

=x^2+y^2+4z^2+4xz-2xy-4yz

8) (x+y) 2 = 4, that is, x 2+2xy+y 2 = 4 ①.

(x-y) 2 = 10, that is, x 2-2xy+y 2 =10 ②.

①+②, 2x 2+2y 2 = 14, then x 2+y 2 = 7.

①-②, 4xy=-6, then xy= -3/2.

The answer is difficult. It's up to you whether to adopt it or not.