First: Use Distributive Property
[tex]3 \sqrt{10} (5 \sqrt{2} - 6 \sqrt{8}) \\ 3 \sqrt{10} (5 \sqrt{2} - 6 \sqrt{4 \times 2} ) \\ 3 \sqrt{10} (5 \sqrt{2} - 12 \sqrt{2} ) \\ 3 \sqrt{10} (5 - 12( \sqrt{2} ) \\ 3 \sqrt{10} ( - 7 \sqrt{2} ) \\ ( 3 \times - 7)( \sqrt{10} \times \sqrt{2} ) \\ - 21 \sqrt{20} \\ - 21 \sqrt{5 \times 4 } \\ - 21 \times 2 \sqrt{5} \\ - 42 \sqrt{5} [/tex]
Second: FOIL Method
[tex](5 \sqrt{x} - 4 \sqrt{y} )(3 \sqrt{x} - 8 \sqrt{y} ) \\ 15x - 40 \sqrt{xy} - 12 \sqrt{xy} + 32y \\ 15x - 52 \sqrt{xy} + 32y[/tex]
Third: Square of a Binomial
[tex]( \sqrt{3x - 5} - 4)^{2} \\ ( \sqrt{3x - 5} )^{2} + 2( - 4)( \sqrt{3x - 5} ) + ( - 4)^{2} \\ 3x - 5 - 8 \sqrt{3x - 5} + 16 \\ 3x - 5 + 16 - 8 \sqrt{3x - 5} \\ 3x + 11 - 8 \sqrt{3x - 5} [/tex]
