ShmoopTube

00:04

Multiplying Polynomials, a la Shmoop.

00:07

Shmonet<<shmo-nay>>, the famous cartoon muralist…

00:10

…wants to be in the Guinness Book of World Records for making the biggest mural.

00:15

He had some bad experiences in the past with the metric system…

00:18

…don’t ask, he doesn’t like to talk about it…

00:20

…so he measures practically everything in terms of the length of his longest paintbrush,

00:25

which we can call p.

00:28

In order to submit his mural, he needs to find the equation for the area of his mural, in terms of “p.”

00:36

He measures the length of one side as p plus 3...

00:41

…and the width as p-squared minus 4p plus 2.

00:46

Knowing that the area formula is length times width,

00:50

multiplying the two will give him the area of the world record mural.

00:55

We can find the product between the two polynomials by splitting up the p plus 3…

01:01

…to get p times p-squared minus 4p plus 2…

01:05

plus 3 times p-squared minus 4p plus 2.

01:10

Using the distributive property we can start distributing.

01:15

P times p squared equals p-cubed, plus p times negative 4p

01:20

which is negative 4p squared, plus p times 2 equals 2p…

01:27

…PLUS 3 times p squared is 3p squared...

01:31

...plus 3 times negative 4p is minus 12p plus 3 times 2 which is 6.

01:40

Now we can combine like terms.

01:42

There's no other p-cubed terms, so we can leave it as p-cubed.

01:46

We have two p squared terms, negative 4p squared and 3p squared.

01:51

So let's combine like terms.

01:53

Negative 4p squared plus 3p squared equals negative p squared.

01:57

We have two p terms, so we again can combine like terms.

02:01

2p minus 12p equals negative 10p.

02:05

We only have one constant number, 6, so we can just leave that as it is.

02:10

After we combine all like terms we get the answer as

02:13

p cubed minus p squared minus 10 p plus 6.

02:20

Poor Shmonet. It seems his paintbrush is roughly the length of a toothpick.

02:24

Well, that’s just one more thing he can bring up in therapy.

Full Transcript