Question

How do you simplify `(sqrt5-2)(sqrt5+2)`?

Answer 1

See a solution process below:

Explanation:

Use this rule for quadratics for this special case:

`(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2`

Let:

• `color(red)(sqrt(5)) = color(red)(x)`
• `color(blue)(2) = color(blue)(y)`

Substitute as:

`(color(red)(sqrt(5)) + color(blue)(2))(color(red)(sqrt(5)) - color(blue)(2)) =>`

`(color(red)(sqrt(5)))^2 - color(blue)(2)^2 =>`

`5 - 4 =>`

`1`