Question

Срочно пж номер 717. Плиизз

Answer 1

$1)\; \; (x^2-2x+1)(x^2+2x+1)=(x^2+1)^2-(2x)^2=\\\\=x^4+2x^2+1-4x^2=x^4-2x^2+1=(x^2-1)^2\\\\2)\; \; (2t-v+s)(t+2v-s)=\Big (t+[\, t-(v-s)]\Big )\Big (v+[\, t+(v-s)]\Big )=\\\\=tv+t(t+v-s)+(t-v+s)v+\Big (t^2-(v-s)^2\Big )=\\\\=tv+t^2+tv-ts+tv-v^2+vs+t^2-(v^2-2vs+s^2)=\\\\=2t^2+-2v^2-s^2+3tv+3vs-ts\\\\3)\; \; (y^2-3y-2)(y^2+3y-2)=\Big ((y^2-2)-3y\Big )\Big ((y^2-2)+3y\Big )=\\\\=(y^2-2)^2-(3y)^2=y^4-4y^2+4-9y^2=y^4-13y^2+4\\\\4)\; \; (a+2b+3c)(2a-b+2c)=\\\\=2a^2-ab+2ac+4ab-2b^2+4bc+6ac-3bc+6c^2=\\\\=2a^2-3b^2+6c^2+3ab+8ac+bc$