1) (a+2b)(a-2b)-(a-b)^ 2) (y+x)^-(y-x)^ 3) (a-2b)^+(a-2b) 4) (a-5x)^+(a+5x)^ 5)...

Решите задачу:

$1)\; \; (a+2b)(a-2b)-(a-b)^2=a^2-4b^2-(a^2-2ab+4b^2)=\\\\=2ab-8b^2=2b(a-4b)\\\\2)\; \; (y+x)^2-(y-x)^2=(y^2+2yx+x^2)-(y^2-2yx+x^2)=\\\\=4yx\\\\3)\; \; (a-2b)^2+(a-2b)=(a-2b)(a-2b+1)\\\\4)\; \; (a-5x)^2+(a+5x)^2=\\\\=a^2-10ax+25x^2+a^2+10ax+25x^2=2a^2+50x^2=\\\\=2(a^2+25x^2)$

$5)\; \; (b-1)(b+1)-(a+1)(a-1)=\\\\=b^2-1-(a^2-1)=b^2-a^2=(b-a)(b+a)\\\\6)\; \; (3a-2)(3a+2)+(a+8)(a-8)=\\\\=9a^2-4+a^2-64=10a^2-68=(\sqrt{10}a-\sqrt{68})(\sqrt{10}a+\sqrt{68})$