Упр.795(стар учебник) ГДЗ Дорофеев Суворова 7 класс (Алгебра)

а) (2n + 3)(n + 1) + (4n — 1)(n — 1) + 2;
б) (2n2 — 1)(n + 1) — (n2 + 1)(2n — 1);
в) ((b + с)2 — (b2 + с2))3 — (3bс)3;
г) ((m — n)2 + 2mn)3 — 3m2n2(m2 + n2);
д) ((x — y)3 + 3хy(х — y))2 + 2x3y3;
е) ((у + z)3 — (у3 + z3))2 — 18у3z3.

1. а)

   $$ (2n+3)(n+1)+(4n-1)(n-1)+2= $$

   $$ =2n^2+2n+3n+3+4n^2-4n-n+1+2=6n^2+6. $$

2. б)

   $$ (2n^2-1)(n+1)-(n^2+1)(2n-1)= $$

   $$ =2n^3+2n^2-n-1-(2n^3-n^2+2n-1)= $$

   $$ =2n^3+2n^2-n-1-2n^3+n^2-2n+1=3n^2-3n. $$

3. в)

   $$ \bigl((b+c)^2-(b^2+c^2)\bigr)^3-(3bc)^3= $$

   $$ =(b^2+2bc+c^2-b^2-c^2)^3-27b^3c^3= $$

   $$ =(2bc)^3-27b^3c^3=8b^3c^3-27b^3c^3=-19b^3c^3. $$

4. г)

   $$ \bigl((m-n)^2+2mn\bigr)^3-3m^2n^2(m^2+n^2)= $$

   $$ =(m^2-2mn+n^2+2mn)^3-3m^4n^2-3m^2n^4= $$

   $$ =(m^2+n^2)^3-3m^4n^2-3m^2n^4= $$

   $$ =m^6+3m^4n^2+3m^2n^4+n^6-3m^4n^2-3m^2n^4=m^6+n^6. $$

5. д)

   $$ \bigl((x-y)^3+3xy(x-y)\bigr)^2+2x^3y^3= $$

   $$ =(x^3-3x^2y+3xy^2-y^3+3x^2y-3xy^2)^2+2x^3y^3= $$

   $$ =(x^3-y^3)^2+2x^3y^3= $$

   $$ =x^6-2x^3y^3+y^6+2x^3y^3=x^6+y^6. $$

6. е)

   $$ \bigl((y+z)^3-(y^3+z^3)\bigr)^2-18y^3z^3= $$

   $$ =(y^3+3y^2z+3yz^2+z^3-y^3-z^3)^2-18y^3z^3= $$

   $$ =(3y^2z+3yz^2)^2-18y^3z^3= $$

   $$ =9y^4z^2+18y^3z^3+9y^2z^4-18y^3z^3=9y^4z^2+9y^2z^4. $$

Ответ

а) $$6n^2+6$$; б) $$3n^2-3n$$; в) $$-19b^3c^3$$; г) $$m^6+n^6$$; д) $$x^6+y^6$$; е) $$9y^4z^2+9y^2z^4$$.