Упр.37.27 ГДЗ Мордкович 10-11 класс (Алгебра)

а) (x^1/3 + 3)(x^1/3 — 3);
б) (a^1/2 + b^1/2)(a — a^1/2 * b^1/2 + b);
в) (d^1/2 — 1)(d^1/2 + 1);
г) (p^1/3 — q^1/3)(p^2/3 + (pq)^1/3 + q^2/3).

1. а)
   $$\left(x^{\frac13}+3\right)\left(x^{\frac13}-3\right)=\left(x^{\frac13}\right)^2-3^2=x^{\frac23}-9.$$

2. б)
   $$\left(a^{\frac12}+b^{\frac12}\right)\left(a-a^{\frac12}b^{\frac12}+b\right)$$
   $$=a^{\frac32}-a b^{\frac12}+a^{\frac12}b-a^{\frac12}b+b^{\frac32}$$
   $$=a^{\frac32}+b^{\frac32}.$$

3. в)
   $$\left(d^{\frac12}-1\right)\left(d^{\frac12}+1\right)=\left(d^{\frac12}\right)^2-1^2=d-1.$$

4. г)
   $$\left(p^{\frac13}-q^{\frac13}\right)\left(p^{\frac23}+(pq)^{\frac13}+q^{\frac23}\right)$$
   $$=p-p^{\frac23}q^{\frac13}+p^{\frac13}q^{\frac13}p^{\frac23}+p^{\frac13}q^{\frac13}q^{\frac23}-p^{\frac23}q^{\frac13}-q$$
   $$=p-q.$$

Ответ

а) $$x^{\frac23}-9$$; б) $$a^{\frac32}+b^{\frac32}$$; в) $$d-1$$; г) $$p-q$$.