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(male narrator) In this video,
we will look at using the perfect square shortcut
to square binomial radical expressions.
You may recall, when we're squaring a binomial,
we end up with the first term squared,
but then we have the product-- a times b--there twice.
This means, we have 2 times the product ab.
And then, finally, we square the last term.
It is important to note, we don't simply square both terms,
but we also have that important middle term "twice the product."
We also must always be sure
our final answer, as always, is reduced.
Let's take a look at some problems
where we square with radical expressions.
Here, we are asked to square this expression.
We first will square the first term.
Remember that square and square root
are inverses of each other.
If we take the square root of 6 and square it,
the square and square root undo each other,
leaving us just the 6 behind.
In the center, we need twice the product:
root 6 times -root 2 is -root 12.
And it is there twice: -root 2, root 12.
Again, we'll square the last term at the end,
and just as before, when we square a square root,
the square and the square root undo each other,
leaving just the +2.
When we combine like terms: 6 plus 2 is 8, minus 2 root 12.
We also want to simplify that root 12.
The prime factorization of 12...
can be quickly calculated to be 2 squared times 3:
8 minus 2 root 2 squared, times 3,
and then we can take
the 2 squared out as a 2 to the first power.
We now have 8 minus 4, square root of 3,
for our final answer.
Let's take a look at another problem
where we have to square a binomial
using this shortcut pattern.
Again, we'll start by squaring the first number:
2 squared is 4.
Then, we take twice the product:
2 times 3 root 7 is 6 root 7.
It's there twice, so 6 and 6 gives us +12 of these root 7s.
Finally, we'll square the last term:
3 squared is 9, and when we square the square root of 7,
the square root and square are inverses, leaving just the 7.
Now, we just have to simplify what's left
by multiplying 9 times 7,
and we have 4 plus 12 root 7, plus 63.
Combining like terms, we get our final answer:
67 plus 12 root 7.
By remembering our square shortcut,
we can square the first term, take the product twice,
and then square the last term.
Always make sure your final answer is reduced,
and you'll have your final answer.