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

1. Упростите выражение:
   
   а) $$(2n+3)(n+1)+(4n-1)(n-1)+2$$;
   
   б) $$(2n^2-1)(n+1)-(n^2+1)(2n-1)$$;
   
   в) $$\bigl((b+c)^2-(b^2+c^2)\bigr)^3-(3bc)^3$$;
   
   г) $$\bigl((m-n)^2+2mn\bigr)^3-3m^2n^2(m^2+n^2)$$;
   
   д) $$\bigl((x-y)^3+3xy(x-y)\bigr)^2+2x^3y^3$$;
   
   е) $$\bigl((y+z)^3-(y^3+z^3)\bigr)^2-18y^3z^3$$.

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) $$9y^4z^2+9y^2z^4$$.