Упр.393 ГДЗ Никольский Потапов 9 класс (Алгебра)

393.
а) x^(1/2) y^(1/2) (x^(1/2)-y^(1/2))
б) (a^(1/2)-1)(a^(1/2)+1)
в) (x^(1/2)-y^(1/2))(x^(1/2)+y^(1/2))
г) (m^(1/2)+3)(m^(1/2)-3)

1. $$x^{\frac12}y^{\frac12}(x^{\frac12}-y^{\frac12})=x^{\frac12}y^{\frac12}\cdot x^{\frac12}-x^{\frac12}y^{\frac12}\cdot y^{\frac12}=xy^{\frac12}-x^{\frac12}y.$$

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

3. $$\left(x^{\frac12}-y^{\frac12}\right)\left(x^{\frac12}+y^{\frac12}\right)=\left(x^{\frac12}\right)^2-\left(y^{\frac12}\right)^2=x-y.$$

4. $$\left(m^{\frac12}+3\right)\left(m^{\frac12}-3\right)=\left(m^{\frac12}\right)^2-3^2=m-9.$$

Ответ

а) $$xy^{\frac12}-x^{\frac12}y$$; б) $$a-1$$; в) $$x-y$$; г) $$m-9$$.