\[\boxed{\text{494\ (494).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\mathbf{Вспомним:}\]
\[\sqrt{\mathbf{a}}\mathbf{\cdot}\sqrt{\mathbf{b}}\mathbf{=}\sqrt{\mathbf{\text{ab}}}\mathbf{;\ \ }\]
\[\mathbf{при\ }\mathbf{a \geq 0;\ \ b \geq 0.}\]
\[\mathbf{Свойство\ степеней:}\]
\[\mathbf{a}^{\mathbf{m + n}}\mathbf{=}\mathbf{a}^{\mathbf{m}}\mathbf{\cdot}\mathbf{a}^{\mathbf{n}}\mathbf{.}\]
\[\mathbf{Формулы\ суммы\ и\ разности\ }\]
\[\mathbf{кубов:}\]
\[\left( \mathbf{a - b} \right)\left( \mathbf{a}^{\mathbf{2}}\mathbf{+ ab +}\mathbf{b}^{\mathbf{2}} \right)\mathbf{=}\]
\[\mathbf{=}\mathbf{a}^{\mathbf{3}}\mathbf{-}\mathbf{b}^{\mathbf{3}}\mathbf{;}\]
\[\left( \mathbf{a + b} \right)\left( \mathbf{a}^{\mathbf{2}}\mathbf{- ab +}\mathbf{b}^{\mathbf{2}} \right)\mathbf{=}\]
\[\mathbf{=}\mathbf{a}^{\mathbf{3}}\mathbf{+}\mathbf{b}^{\mathbf{3}}\mathbf{.}\]
Решение.
\[\textbf{а)}\ \left( 1 - \sqrt{x} \right)\left( 1 + \sqrt{x} + x \right) =\]
\[= 1^{3} - \left( \sqrt{x} \right)^{3} = 1 - x\sqrt{x}.\]
\[\textbf{б)}\ \left( \sqrt{a} + 2 \right)\left( a - 2\sqrt{a} + 4 \right) =\]
\[= \left( \sqrt{a} \right)^{3} + 2^{3} = a\sqrt{a} + 8.\]
\[= 8 + a\sqrt{a}\]
\[\textbf{в)}\ \left( \sqrt{m} - \sqrt{n} \right)\left( m + n + \sqrt{\text{mn}} \right) =\]
\[= \left( \sqrt{m} \right)^{3} - \left( \sqrt{n} \right)^{3} =\]
\[= m\sqrt{m} + n\sqrt{n}\]
\[\textbf{г)}\ \left( x + \sqrt{y} \right)\left( x^{2} + y - x\sqrt{y} \right) =\]
\[= x^{3} + \left( \sqrt{y} \right)^{3} = x^{3} + y\sqrt{y}\]