1、（a-b+1）（a+b-1）
=[(a-(b-1)](a+b-1)
=a^2-(b-1)^2
=a^2-b^2+2b-1
2、(x+1)(x的平方+1)(x的4次方+1)(x-1)
=(x-1)(x+1)(x^2+1)(x^4+1)
=(x^2-1)(x^2+1)(x^4+1)
=(x^4-1)(x^4+1)
=x^8-1
3、(a-2b+3)(a+2b-3)
=[a-(2b-3)](a+2b-3)
=a^2-(2b-3)^2
=a^2-4b^2+12b-9
4、[(x-y)^2+(x+y)^2](x^2-y^2)
=[(x^2-2xy+y^2)+(x^2+2xy+y^2)](x^2-y^2)
=(2x^2+2y^2)(x^2-y^2)
=2(x^2+y^2)(x^2-y^2)
=2(x^4-y^4)
=2x^4-2y^4