1. 计算:
(1)$(5x+y)(5x-y)$; (2)$(-1+3x)(-3x-1)$;
(3)$(-2b-7)(2b-7)$; (4)$201×199$;
(5)$2003^{2}-1997^{2}$; (6)$100^{2}-103×97$;
(7)$(x-3)(x+3)+x(2-x)$; (8)$(3x+y)(y-3x)-4y(x-y)$;
(9)$x(x+1)-(x-12)(x+12)$; (10)$(x-2)(x+8)-(3x+4)(3x-4)$;
(11)$(x-2y)(x^{2}+4y^{2})(x+2y)$; (12)$(x-2)(x+2)(x^{2}-4)$.
答案：1.解:(1)原式$=(5x)^{2}-y^{2}=25x^{2}-y^{2}.$
(2)原式$=(-1)^{2}-(3x)^{2}=1-9x^{2}.$
(3)原式$=49-4b^{2}.$
(4)原式$=(200+1)(200-1)=40000-1=39999.$
(5)原式$=(2003+1997)(2003-1997)=24000.$
(6)原式$=100^{2}-(100+3)(100-3)=100^{2}-(100^{2}-3^{2})=9.$
(7)原式$=x^{2}-9+2x-x^{2}=2x-9.$
(8)原式$=y^{2}-(3x)^{2}-4xy+4y^{2}=y^{2}-9x^{2}-4xy+4y^{2}=$
$5y^{2}-9x^{2}-4xy.$
(9)原式$=x^{2}+x-x^{2}+144=x+144.$
(10)原式$=x^{2}+6x-16-9x^{2}+16=-8x^{2}+6x.$
(11)原式$=(x-2y)(x+2y)(x^{2}+4y^{2})=(x^{2}-4y^{2})(x^{2}+$
$4y^{2})=x^{4}-16y^{4}.$
(12)原式$=(x^{2}-4)(x^{2}-4)=x^{4}-8x^{2}+16.$
2. (2024春·竞秀区校级月考)已知$m+n= 7,m-n= 3$,求代数式$m^{2}-n^{2}$的值.
答案：2.解:$\because m+n=7,m-n=3,$
$\therefore m^{2}-n^{2}=(m+n)(m-n)=7×3=21.$
