Question

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

Answer 1

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)`