Question

How do you simplify `(sqrt5+4)(sqrt5-1)`?

Answer 1

See the entire 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(5)) + color(red)(4))(color(blue)(sqrt(5)) - color(blue)(1))` becomes:

`(color(red)(sqrt(5)) xx color(blue)(sqrt(5))) - (color(red)(sqrt(5)) xx color(blue)(1)) + (color(red)(4) xx color(blue)(sqrt(5))) - (color(red)(4) xx color(blue)(1))`

`(sqrt(5))^2 - sqrt(5) + 4sqrt(5) - 4`

`5 - sqrt(5) + 4sqrt(5) - 4`

We can now group and combine like terms:

`5 - 4 - 1sqrt(5) + 4sqrt(5)`

`(5 - 4) + (-1 + 4)sqrt(5)`

`1 + 3sqrt(5)`

Or

`3sqrt(5) + 1`

Answer 2

`1+3sqrt(5)`

Explanation:

`(sqrt(5)+4)(sqrt(5)-1)=`

`=5-sqrt(5)+4sqrt(5)-4=`

`=1+3sqrt(5)`