Question

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

Answer 1

Distribute the one expression over the other, then add the resulting terms together, to get to `-7`

Explanation:

Let's start with the original expression:

`(sqrt2-3)(sqrt2+3)`

Now let's distribute the one over the other. I'll list the answers below:

`sqrt2*sqrt2=2`
`sqrt2*3=3sqrt2`
`-3*sqrt2=-3sqrt2`
`-3*3=-9`

We can now add them up:

`2+3sqrt2-3sqrt2-9`

The square root terms subtract against each other and so drop off. We're left with `2-9=-7`