1.计算:
(1)(a-2b+1)(a+2b+1);
(2)(x+2y-1)²;
(3)(x-1)²(x+1)²(x²+1)²;
(4)(2x-1)²-(x-2)².
答案：(1)$a^2+2a+1-4b^2$
(2)$x^2+4y^2+4xy-2x-4y+1$
(3)$x^8-2x^4+1$
(4)$3x^2-3$
2.计算:$(x+y+z)(x+y-z)-(x+y+z)^2$
答案：$-2z^2-2xz-2yz$
3.计算:$(x-2y-z)(x+2y-z)-(x+z)^2$
答案：$-4xz-4y^2$
4.计算:$(2^4 - 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1).$
答案：解:原式=$(2^8-1)(2^8+1)(2^{16}+1)(2^{32}+1)=(2^{16}-1)·(2^{16}+1)(2^{32}+1)=(2^{32}-1)(2^{32}+1)=2^{64}-1.$
5.已知代数式$(m-1)^2 + (m+n)(m-n) + n^2$.
(1)化简这个代数式；
(2)若$m^2 - m -3=0$,求这个代数式的值.
答案：解:(1)$(m-1)^2+(m+n)(m-n)+n^2$
$=m^2-2m+1+m^2-n^2+n^2$
$=2m^2-2m+1.$
(2)$\because m^2 - m -3=0,$
$\therefore m^2 - m=3,$
$\therefore 2m^2-2m+1=2(m^2-m)+1=2×3+1=7.$
