**Video Transcript**

##
Transcript
**Factoring Special Case Polynomials**

Daniella Feinberg, who recently retired from the fur **business**, and her husband are trying to enjoy a relaxing afternoon in front of their **pool**. She wants her husband, who makes a handsome living designing pools, to design one so she can throw a pool party...

What's this? The neighbor's **dog** just came through the fence and it looks like he has plans to do a little bit of surfing...Uh-oh... it looks like this pug's doggie instincts are taking over and he's ripping up the inflatable pool! I guess he's all about that **pug** life. Daniella's up in arms about the neighbor's dog. I guess her husband has his work cut out for him

### Side lengths of the pool

Mr. Feinberg suggests that they build a square pool with side **lengths** 'a'. Using what we learned about **area**, we know we can find the area by multiplying the two side lengths **together**. Doing so gives us **a²**, but Daniella doesn't like this option because it's too "normal". To make the pool less "normal", Mr. Feinberg suggests side **measurements** of (a - b), giving them a pool area of (a-b)(a - b) or (a - b)².

### The FOIL method

Being the consummate professional, Mr. Feinberg uses the **FOIL method** to figure out exactly what he's dealing with. First he **subtracts** the b term from his existing plans. Since he already knows a(a) is a², he can concentrate on the other **terms**. a(-b) is -ab and since we have this twice, we can write it here...and here.

Finally, he has two '-b's that he needs to **multiply** together, giving him +b². Now he just **adds** all the terms together and combines like terms, leaving him with a² - 2ab + b². Daniella thinks it'd be silly if she threw a pool party with this small of a pool, so then Mr. Feinberg suggests (a + b)(a + b) to give Daniella the biggest pool that'll fit in their yard.

### Write this mathematically

We can write this **mathematically** as (a + b)(a + b) or (a + b)². Mr. Feinberg's training is coming in handy, so when he applies the FOIL method to (a + b)², he knows he'll get a **positive** a² and b² and 'ab' twice gives him 2a making his final **expression** a² + 2ab + b². Since Daniella doesn't want to give up her rose garden, and since square pools are SO five minutes ago, she rejects this option as well.

Then, in a stroke of genius, Mr. Feinberg comes up with (a + b)(a - b). Mr. Feinberg uses the FOIL method one last time and gets a² one '+ab' one '-ab' and a -b². The two 'ab' terms cancel out, leaving Mr. Feinberg with a² - b². He draws it out for Daniella who looks at him quite curiously. She shows him that he's only cut out a little block from the area, not to mention the pool looks funny!

### The area

Eureka again! Mr. Feinberg can move this piece here to make the pool not look as funny! All this talk of As and Bs is making Daniella a bit dizzy. She wants to know the area of the pool so that she can start **planning** the party. The Special Case **Polynomials** that Mr. Feinberg suggested were: a², (a - b)², (a + b)², and (a + b)(a - b).

### Use PEMDAS for calculation

We can use any **numbers** for 'a' and 'b', but we'll use 10 feet for 'a' and 5 feet for 'b'. When we **plug** numbers in, instead of applying FOIL to our expression, we can use **PEMDAS** to make our **calculations** easier. Plugging 10 feet in for 'a' and 5 feet for 'b' gives us 100 ft.² for a² 25 ft.² for (a - b)² 225 ft.² (a + b)² and 75 ft.² for (a + b)(a - b). Good things usually come in threes, and Mr. Feinberg has had another brilliant idea...

All in a hard day's work! They're finally done! Now Daniella can throw her blowout pool party! What's this?!? Looks like a pugly situation...