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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