Tip:
Highlight text to annotate it
X
(male narrator) In this video,
we will look at multiplying a special polynomial
that's called a "sum and a difference."
A sum and a difference is when the two factors match exactly,
except one is a sum-- or with addition--
and one is a difference-- or subtraction.
When we multiply these using FOIL,
we find a times a is a squared, a times -b is minus ab,
b times a is plus ab, and b times -b is -b squared.
What's interesting about this
is the like terms in the middle will subtract out to 0,
leaving just the a squared minus b squared.
This is where we get our shortcut
to multiply a sum and a difference:
a plus b, times a, minus b.
Instead of going through all the steps of FOIL,
we will simply multiply
the first two together to get the a squared
and the last two together to get the -b squared.
We can use this shortcut, because we know
that the sum and difference is going to cause
the middle terms to subtract out.
Let's take a look at some examples
where we can see this worked out.
In this problem, notice the factors are identical,
except one is a sum, and one is a difference.
Here, we can just multiply the first two together:
x times x to get x squared;
and the last two together: 5 times -5 is -25.
And we have our product.
Let's try another example that may be slightly more involved.
Again, in this problem,
we notice the two factors are identical,
except one is a sum, and one is a difference.
This allows us to use the sum and difference shortcut,
multiplying the first by the first:
6x times 6x is 36, x squared.
And the last times the last: 2 times -2 is -4.
And that becomes our product.
If we recognize the sum and difference,
we can save ourselves time as we multiply out our solution.