Now it should be pointed out, that these binomials are special and that we're

multiplying together the difference and sum of the same two terms.

We have 2x and 2x and 1, and 1. And there's a special formula in this

type of case. And the formula, is that A - B * A + B =

A^2 - b^2 because the outer and inner terms will always cancel, which is what

we just saw. That is, in our case, our A = 2x and our

B = 1. So our answer here is A^2 - b^2 or 2x^2 -

1^2 which is this 4x^2 - 1. Let's do another example.

Now be careful here with this power of 2, we cannot apply that to each of these two

terms. What this means is 3y - 5 * 3y - 5.

So, again we can FOIL. This is equal to the product of the first

terms in the two binomials, so 3y * 3y and then plus the product of the outer

terms in the two binomials, so 3y * -5 and then plus the product of the inner

terms in the two binomials. So -5 * 3y and then plus the product of

the last terms in the two binomials. So -5 * -5 which is equal to 9y^2 - 15y -

15y + 25. And combining the outer and inner terms

gives us our answer of 9y^2-30y+25. Now again, this is the common type of

multiplication here where we're multiplying a binomial by itself and

there's a special formula again in this type of case.

And the formula is that (A - B)^2 = A^2 - 2AB + B^2.

That is the outer and inner terms are the same, so there'll be two of them, which

we just saw with A = 3y and b = 5. So, our answer here is A^2 or 3y^2 - 2 *

A * B + B^2 or 9y^2 - 30y + 25. And this how we multiplied two binomials.

Thank you, and we'll see you next time. [SOUND]