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

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Answer 1 · 2016-05-29T13:59:25

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

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 $2-9=-7$

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