How do you simplify #(5 + 2sqrt2)(8 - 3sqrt2)#?

1 Answer
smendyka
Jul 19, 2018

See a solution 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)(5) + color(red)(2sqrt(2)))(color(blue)(8) - color(blue)(3sqrt(2)))# becomes:

#(color(red)(5) xx color(blue)(8)) - (color(red)(5) xx color(blue)(3sqrt(2))) + (color(red)(2sqrt(2)) xx color(blue)(8)) - (color(red)(2sqrt(2)) xx color(blue)(3sqrt(2)))#

#40 - 15sqrt(2) + 16sqrt(2) - 6(sqrt(2))^2#

#40 + (-15 + 16)sqrt(2) - (6 xx 2)#

#40 + 1sqrt(2) - 12#

#40 + sqrt(2) - 12#

#40 - 12 + sqrt(2)#

#28 + sqrt(2)#

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