Multiply the radical expressions. $$( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )$$
A) $- 16$
B) $16 \sqrt { 15 } + 4 \sqrt { 5 } - 48 \sqrt { 3 } - 12$
C) $32 \sqrt { 15 } + 8 \sqrt { 5 } - 192 \sqrt { 3 } - 12$
D) $16 \sqrt { 15 } - 12$

Question

Quizplus · Accepted Answer

To multiply the given radical expressions, use the distributive property (FOIL method for binomials): $(4\sqrt{6} + \sqrt{2})(2\sqrt{10} - 3\sqrt{8})$. Multiply each term in the first expression by each term in the second expression and simplify: $4\sqrt{6} \cdot 2\sqrt{10} = 8\sqrt{60} = 16\sqrt{15}$, $4\sqrt{6} \cdot (-3\sqrt{8}) = -12\sqrt{48} = -24\sqrt{12} = -48\sqrt{3}$, $\sqrt{2} \cdot 2\sqrt{10} = 2\sqrt{20} = 4\sqrt{5}$, and $\sqrt{2} \cdot (-3\sqrt{8}) = -3\sqrt{16} = -12$. Adding these results gives $16\sqrt{15} + 4\sqrt{5} - 48\sqrt{3} - 12$.

Multiply the Radical Expressions (46+2)(210−38)( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )(46​+2​)(210​−38​)

Multiply the Radical Expressions $( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )$