Упр.14.11 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) a^(n+1)+a^n+a+1;
2) b^(n+2)-b-1+b^(n+1);
3) 3y^(n+3)-3y^2-5+5y^(n+1).

1. $$a^{n+1}+a^n+a+1=a^n(a+1)+(a+1)=(a+1)(a^n+1).$$

2. $$b^{n+2}-b-1+b^{n+1}=(b^{n+2}+b^{n+1})-(b+1)=b^{n+1}(b+1)-(b+1)=(b+1)(b^{n+1}-1).$$

3. $$3y^{n+3}-3y^2-5+5y^{n+1}=3y^2(y^{n+1}-1)+5(y^{n+1}-1)=(y^{n+1}-1)(3y^2+5).$$

Ответ

1) $$\left(a+1\right)\left(a^n+1\right);$$
2) $$\left(b+1\right)\left(b^{n+1}-1\right);$$
3) $$\left(y^{n+1}-1\right)\left(3y^2+5\right).$$