Question

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

Answer 1

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)`