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

1 Answer

Answer:

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#