Упр.63 ГДЗ Алимов 10-11 класс (Алгебра)

Вынести общий множитель за скобки:

1. $$x^{1/2}+x$$;
2. $$(ab)^{1/3}+(ac)^{1/3}$$;
3. $$y^{3/4}-y^{1/3}$$;
4. $$12xy^{1/2}-3x^{1/2}y$$.

1. $$x^{\frac12}+x=x^{\frac12}+x^{\frac12}\cdot x^{\frac12}=x^{\frac12}\left(1+x^{\frac12}\right).$$

2. $$\left(ab\right)^{\frac13}+\left(ac\right)^{\frac13}=a^{\frac13}b^{\frac13}+a^{\frac13}c^{\frac13}=a^{\frac13}\left(b^{\frac13}+c^{\frac13}\right).$$

3. $$y^{\frac34}-y^{\frac13}=y^{\frac{9}{12}}-y^{\frac{4}{12}}=y^{\frac{4}{12}}\left(y^{\frac{5}{12}}-1\right)=y^{\frac13}\left(y^{\frac{5}{12}}-1\right).$$

4. $$12xy^{\frac12}-3x^{\frac12}y=3x^{\frac12}y^{\frac12}\left(4x^{\frac12}-y^{\frac12}\right).$$