How do you evaluate #(5\sqrt { 7} - \sqrt { 3} ) ( 8\sqrt { 3} - 7\sqrt { 7} )#?

1 Answer
smendyka
Oct 31, 2017

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(5sqrt(7)) - color(red)(sqrt(3)))(color(blue)(8sqrt(3)) - color(blue)(7sqrt(7)))# becomes:

#(color(red)(5sqrt(7)) xx color(blue)(8sqrt(3))) - (color(red)(5sqrt(7)) xx color(blue)(7sqrt(7))) - (color(red)(sqrt(3)) xx color(blue)(8sqrt(3))) + (color(red)(sqrt(3)) xx color(blue)(7sqrt(7)))#

#40sqrt(7)sqrt(3) - 35sqrt(7)^2 - 8sqrt(3)^2 + 7sqrt(3)sqrt(7)#

#40sqrt(21) - (35 * 7) - (8 * 3) + 7sqrt(21)#

#40sqrt(21) - 245 - 24 + 7sqrt(21)#

We can now group and combine like terms:

#40sqrt(21) + 7sqrt(21) - 245 - 24#

#(40 + 7)sqrt(21) + (-245 - 24)#

#47sqrt(21) + (-269)#

#47sqrt(21) - 269#

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