How do you evaluate #(8- \sqrt { 7} ) ( 1+ \sqrt { 7} )#?

1 Answer
smendyka
Apr 29, 2017

See the 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)(8) - color(red)(sqrt(7)))(color(blue)(1) + color(blue)(sqrt(7)))# becomes:

#(color(red)(8) xx color(blue)(1)) + (color(red)(8) xx color(blue)(sqrt(7))) - (color(red)(sqrt(7)) xx color(blue)(1)) - (color(red)(sqrt(7)) xx color(blue)(sqrt(7)))#

#8 + 8sqrt(7) - 1sqrt(7) - sqrt(7)^2#

#8 + 8sqrt(7) - 1sqrt(7) - 49#

We can now combine like terms:

#8 + (8 - 1)sqrt(7) - 49#

#8 + 7sqrt(7) - 49#

#7sqrt(7) - 41#

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