Perform the indicated operation. Simplify, if possible. $( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )$
A) $63 \sqrt { 2 }$
B) $62 + \sqrt { 2 }$
C) 62
D) $62 + 45 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

To solve this, we use the distributive property (FOIL method for binomials): $(9\sqrt{2} - 7)(5\sqrt{2} + 4)$. First, multiply $9\sqrt{2}$ by $5\sqrt{2}$ to get $45 \times 2 = 90$. Second, multiply $9\sqrt{2}$ by $4$ to get $36\sqrt{2}$. Third, multiply $-7$ by $5\sqrt{2}$ to get $-35\sqrt{2}$. Fourth, multiply $-7$ by $4$ to get $-28$. Adding these results together: $90 + 36\sqrt{2} - 35\sqrt{2} - 28 = 62 + \sqrt{2}$.

Perform the Indicated Operation (92−7)(52+4)( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )(92​−7)(52​+4)

Perform the Indicated Operation $( 9 \sqrt { 2 } - 7 ) ( 5 \sqrt { 2 } + 4 )$