How do you simplify #(sqrt7+5)(sqrt7-5)#?

1 Answer
smendyka
Jan 20, 2017

See the entire simplification process below:

Explanation:

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

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

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

#sqrt(7)^2 - 5sqrt(7) + 5sqrt(7) - 25#

We can now combine like terms:

#7 + (-5 + 5)sqrt(7) - 25#

#7 + 0 - 25#

#-18#

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