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So it's the difference Of two squares. And in this type of situation, there's a

special formula that can help us factor this.

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

And let's think about why this is true. Let's FOIL the right hand side here.

We have A^2+AB-BA-B^2. But AB and BA are the same by

communitivity, so they'll cancel here, and we're just left with the left-hand

side. Okay, let's apply that here with A=8u and

B=5. In other words, this is equal to A-B or

8u-5*A+B, or 8u+5, which would be our answer.

Alright, lets see another special formula.

[SOUND] Let's doctor this expression. Now this is what we call a perfect

square, and there are special formulas here as well.

And the formulas are that A^2+2AB+B^2=(A+B)^2, or

A^2-2AB+B^2=(A-B)^2. Again we can verify these formulas by

foiling out the right hand sides, however we'll just do that with the last one

here. (A-B)^2.

This means (A-B)(A-B)=A^2-AB-BA+B^2, and AB and BA are the same, so we have 2

of them, which is the left hand side here.

Now, a tip that our expression might be of this form is that both the first term

and the last term are perfect squares. That is, this is equal to (2x)²-20x, And

then +5^2. Now with this middle term here, 20 X is

equal to 2 times the product of this and this.

Then it's going to be of this form and, sure enough, this is equal to 2*2*5 is

20. So this is 20x, and because of this

negative here, we'll be using this second formula down here.

In other words, this is of the form A^2-2AB+B^2,

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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]