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(male narrator) In this video,
we will look at multiplying
a special polynomial called a "perfect square."
The idea with a perfect square
is we'll have some binomial that is squared.
Squared simply means that it is multiplied by itself,
so this is really a plus b, times a, plus b.
If we multiply this out with FOIL:
a times a is a squared, a times b is ab,
b times a is another ab, and b times b is b squared.
Notice the like terms in the middle are exactly identical.
Those like terms in the middle come from multiplying
the a and the b together, and it's there twice.
For this reason, we have a middle term,
which is twice the product of ab--
combining the like terms-- plus b squared.
This gives rise to our perfect square shortcut.
If we have a plus b squared, we can multiply them together
by squaring the first term...
and then taking the product--ab--twice:
ab and ab is 2ab.
And finally, we can square the last term to get b squared.
This is a shortcut that becomes very valuable
as we continue studying algebra.
It's one that, if we know well, it will give us an advantage
as we continue moving forward in this course.
Let's try some examples where we can see these worked out.
Here is a problem where we have a binomial square.
To square it, we can square the first term: x squared.
And then, we look at the product: x times -4 is -4x.
And another -4x will give us -8x,
because it's there twice.
And finally, we square the last: -4 squared is +16.
And this becomes our product.
Let's try another example that might be slightly more involved
where we see the binomial squared.
Again in this problem, we can follow the same pattern.
Squaring the first term:
2x squared, 2 squared is 4, x squared.
And then, we look at the product:
2x times 7 is 14x, and another 14x will be +28x.
And then, we square the last term:
squaring 7 will give us 49.
It is important to note that when we square a binomial,
we will always have three terms in our solution.
Quite often, students forget the middle term,
which comes from multiplying the terms together twice.
If we can remember the shortcut: To square the first,
multiply them twice, and square the last;
we can quickly square our binomials.