Упр.13.9 ГДЗ Мерзляк 10 класс Углубленный уровень (Алгебра)

1) (a^0,5-3b^0,3)(2a^0,5+b^0,3); 4) (a^(1/3)+a^(1/2))(a^(2/3)-a^(5/6)+a);
2) (a^(1/3)+b^(1/3))^2; 5) (a^(1/6)+b^(1/6))(a^(1/6)-b^(1/6))(a^(1/3)-b^(1/3));
3) (b^0,4+3)^2-6b^0,4; 6) (x^(2/9)-1)(x^(4/9)+x^(2/9)+1)(x^(2/3)+1).

1. $$\left(a^{0,5}-3b^{0,3}\right)\left(2a^{0,5}+b^{0,3}\right)$$
   $$=2a-3a^{0,5}b^{0,3}+a^{0,5}b^{0,3}-3b^{0,6}$$
   $$=2a-2a^{0,5}b^{0,3}-3b^{0,6}.$$
2. $$\left(a^{\frac13}+b^{\frac13}\right)^2$$
   $$=a^{\frac23}+2a^{\frac13}b^{\frac13}+b^{\frac23}.$$
3. $$\left(b^{0,4}+3\right)^2-6b^{0,4}$$
   $$=b^{0,8}+6b^{0,4}+9-6b^{0,4}$$
   $$=b^{0,8}+9.$$
4. $$\left(a^{\frac13}+a^{\frac12}\right)\left(a^{\frac23}-a^{\frac56}+a\right)$$
   $$=a+a^{\frac32}+a^{\frac76}-a^{\frac43}-a^{\frac43}+a^{\frac32}$$
   $$=a-2a^{\frac43}+2a^{\frac32}.$$
5. $$\left(a^{\frac16}+b^{\frac16}\right)\left(a^{\frac16}-b^{\frac16}\right)\left(a^{\frac13}-b^{\frac13}\right)$$
   $$=\left(a^{\frac13}-b^{\frac13}\right)\left(a^{\frac13}-b^{\frac13}\right)$$
   $$=\left(a^{\frac13}-b^{\frac13}\right)^2$$
   $$=a^{\frac23}-2a^{\frac13}b^{\frac13}+b^{\frac23}.$$
6. $$\left(x^{\frac29}-1\right)\left(x^{\frac49}+x^{\frac29}+1\right)\left(x^{\frac23}+1\right)$$
   $$=\left(x^{\frac23}-1\right)\left(x^{\frac23}+1\right)$$
   $$=x^{\frac43}-1.$$

Ответ

1) $$2a-2a^{0,5}b^{0,3}-3b^{0,6}$$
2) $$a^{\frac23}+2a^{\frac13}b^{\frac13}+b^{\frac23}$$
3) $$b^{0,8}+9$$
4) $$a-2a^{\frac43}+2a^{\frac32}$$
5) $$a^{\frac23}-2a^{\frac13}b^{\frac13}+b^{\frac23}$$
6) $$x^{\frac43}-1$$