How do you simplify #(7 +3sqrt2)(9- 5sqrt2)#?

1 Answer
smendyka
Jun 1, 2017

See a solution process below:

Explanation:

First, we need to multiply the two parenthetical terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(7) + color(red)(3sqrt(2)))(color(blue)(9) - color(blue)(5sqrt(2)))# becomes:

#(color(red)(7) xx color(blue)(9)) - (color(red)(7) xx color(blue)(5sqrt(2))) + (color(red)(3sqrt(2)) xx color(blue)(9)) - (color(red)(3sqrt(2)) xx color(blue)(5sqrt(2)))#

#63 - 35sqrt(2) + 27sqrt(2) - 15(sqrt(2))^2#

#63 - 35sqrt(2) + 27sqrt(2) - (15 * 2)#

#63 - 35sqrt(2) + 27sqrt(2) - 30#

We can now combine like terms:

#(63 - 30) + (-35 + 27)sqrt(2)#

#33 + (-8)sqrt(2)#

#33 - 8sqrt(2)#

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