Question

How do you simplify `(sqrt6-3)(sqrt6+4)`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(sqrt(6)) - color(red)(3))(color(blue)(sqrt(6)) + color(blue)(4))` becomes:

`(color(red)(sqrt(6)) xx color(blue)(sqrt(6))) + (color(red)(sqrt(6)) xx color(blue)(4)) - (color(red)(3) xx color(blue)(sqrt(6))) - (color(red)(3) xx color(blue)(4))`

`6 + 4sqrt(6) - 3sqrt(6) - 12`

We can now group and combine like terms:

`6 - 12 + 4sqrt(6) - 3sqrt(6)`

`(6 - 12) + (4 - 3)sqrt(6)`

`-6 + 1sqrt(6)`

`-6 + sqrt(6)`