[tex]a^3+b^3= (a+b)(a^2-ab+b^2) \\a^3-b^3= (a-b)(a^2+ab+b^2) \\ \\ \\ (\sqrt{24} + \sqrt{9} )(24+9- \sqrt{24*9})= \\ = (\sqrt{24} + \sqrt{9} )((\sqrt{24} )^2- \sqrt{24}* \sqrt{9} +( \sqrt{9})^2)=( \sqrt{24} )^3+ (\sqrt{9} )^3 \\ \\( \sqrt{24} - \sqrt{9} )(24+9+\sqrt{24*9})= \\ = (\sqrt{24} - \sqrt{9} )((\sqrt{24} )^2+ \sqrt{24}* \sqrt{9} +( \sqrt{9})^2)=( \sqrt{24} )^3- (\sqrt{9} )^3 \\ [/tex]
[tex] ( \sqrt{24} + \sqrt{9} )(24+9- \sqrt{24*9}) -( \sqrt{24} - \sqrt{9} )(24+9+\sqrt{24*9)}= \\ =( \sqrt{24} )^3+ (\sqrt{9} )^3-(( \sqrt{24} )^3- (\sqrt{9} )^3)= \\ =( \sqrt{24} )^3+ (\sqrt{9} )^3-( \sqrt{24} )^3+ (\sqrt{9} )^3=(\sqrt{9} )^3+(\sqrt{9} )^3=2( \sqrt{9})^3= \\ =2* (\sqrt{3^2} )^3=2*3^3=2*27=54[/tex]
