Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$
A) $- 112 \sqrt { 77 } - 44 \sqrt { 7 } + 980 \sqrt { 11 } + 385$
B) $112 \sqrt { 77 } - 44 \sqrt { 11 } - 980 \sqrt { 7 } + 385$
C) $16 \sqrt { 7 } + 4 \sqrt { 11 } - 385$
D) $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385 \sqrt { 343 }$
E) $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385$

Question

Quizplus · Accepted Answer

First, simplify the radicals: $\sqrt{77} = \sqrt{7 \cdot 11}$, $\sqrt{343} = \sqrt{7^3} = 7\sqrt{7}$. Then, multiply the expressions: $(4\sqrt{11} - 5\sqrt{7 \cdot 11})(4\cdot 7\sqrt{7} + \sqrt{7 \cdot 11})$. Distribute and simplify to get $112\sqrt{77} + 44\sqrt{7} - 980\sqrt{11} - 385$.

Find the Following Product and Express Your Answer in Simplest (411−577)(4343+77)( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )(411​−577​)(4343​+77​)

Find the Following Product and Express Your Answer in Simplest $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$