Now sometimes it's hard for students to recognize these perfect square forms.

If you didn't notice, that this was of this form, you could have factored in

other ways and you would have gotten to the same answer but it is very useful if

you can recognize these forms. Let's see another one.

[SOUND] Let's factor this expression. Now this is what we call a sum of 2

cubes. In other words, this is equal to

(2X)^3+(y^2)^2. And again, there's a special formula in

this case, and the formula is that A^3+B^3=(A+B)(A^2-AB)+B^2.

Now there's also formula for the difference of two cubes.

And although wer're not going to be using at here, let's write it anyway.

It states that, A ^ 3 - B ^ 3 = A - B. * a^2 + ab + b^2.

Notice on this first formula, we have a plus here,

and a plus here, but a minus here. Whereas on the second one, we have a

minus here, and a minus here, but a plus here.

Again we can verify these formulas by multiplying out the right hand sides,

but let's just show that with the first one here that we're going to be using.

That is, we have A(A^2-AB+B^2)+B*A^2-AB+B^2, which is

equal to A^3-A^B+AB^2+ BA^2-AB^2+B^3. And the minus A^2B and plus A^2B will

cancel, as well as the AB squared, and minus AB

squared. And we're left with the left hand side of

our formula, A^3+B^3. Okay, so let's apply that here with A=2x

and B=y^2. So by our formula this is equal to, a+b

or 2x+y^2, and then times a^2 which is (2x)^2-a*b,

and then plus b^2, or plus y^2^2, which is equal to

(2x+y^2)(4x^2-2xy^2+y^4), which would be our answer.

So it's very useful to be able to recognize these special factoring

formulas. They can help you out a lot.

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