Упр.347 ГДЗ Никольский Потапов 7 класс (Алгебра)
а) (а + b)2 + (а + b)(а — b);
б) (а + З)2 + (х + 1)2;
в) 2(m+1)2+3(m+2)2;
г) 5(p+q)2+3(p+2q)2;
д) (2а + 3b)2 — (За + 2b)2;
е) 2(3x + у)2- 3(2х + 3у)2;
ж) (m + n)2 + 2(m + n)(2m — n) + (2m — n)2;
з) 2 (р + 3q) (р + 2q)-(p + 2q)2 — (3q + р)2.
$$ (a+b)^2+(a+b)(a-b)=a^2+2ab+b^2+a^2-b^2=2a^2+2ab. $$
$$ (a+3)^2+(x+1)^2=a^2+6a+9+x^2+2x+1=a^2+6a+x^2+2x+10. $$
$$ 2(m+1)^2+3(m+2)^2=2(m^2+2m+1)+3(m^2+4m+4)= $$
$$ =2m^2+4m+2+3m^2+12m+12=5m^2+16m+14. $$
$$ 5(p+q)^2+3(p+2q)^2=5(p^2+2pq+q^2)+3(p^2+4pq+4q^2)= $$
$$ =5p^2+10pq+5q^2+3p^2+12pq+12q^2=8p^2+22pq+17q^2. $$
$$ (2a+3b)^2-(3a+2b)^2=4a^2+12ab+9b^2-9a^2-12ab-4b^2= $$
$$ =-5a^2+5b^2. $$
$$ 2(3x+y)^2-3(2x+3y)^2=2(9x^2+6xy+y^2)-3(4x^2+12xy+9y^2)= $$
$$ =18x^2+12xy+2y^2-12x^2-36xy-27y^2=6x^2-24xy-25y^2. $$
$$ (m+n)^2+2(m+n)(2m-n)+(2m-n)^2= $$
$$ =m^2+2mn+n^2+2(2m^2+mn-n^2)+4m^2-4mn+n^2=9m^2. $$
$$ 2(p+3q)(p+2q)-(p+2q)^2-(3q+p)^2= $$
$$ =2(p^2+5pq+6q^2)-(p^2+4pq+4q^2)-(p^2+6pq+9q^2)= $$
$$ =-q^2. $$
Ответ
а) $$2a^2+2ab$$; б) $$a^2+6a+x^2+2x+10$$; в) $$5m^2+16m+14$$; г) $$8p^2+22pq+17q^2$$; д) $$-5a^2+5b^2$$; е) $$6x^2-24xy-25y^2$$; ж) $$9m^2$$; з) $$-q^2$$.
