Question

How do you simplify `(sqrt7+5)(sqrt7-5)`?

Answer 1

See the entire simplification 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)(sqrt(7)) + color(red)(5))(color(blue)(sqrt(7)) - color(blue)(5))` becomes:

`(color(red)sqrt(7) xx color(blue)(sqrt(7))) - (color(red)(sqrt(7)) xx color(blue)(5)) + (color(red)(5) xx color(blue)(sqrt(7))) - (color(red)(5) xx color(blue)(5))`

`sqrt(7)^2 - 5sqrt(7) + 5sqrt(7) - 25`

We can now combine like terms:

`7 + (-5 + 5)sqrt(7) - 25`

`7 + 0 - 25`

`-18`