ShmoopTube

00:03

Multiplying Polynomials, a la Shmoop.

00:07

Shmonet the famous cartoon muralist… …wants to be in the Guinness Book of World [Shmonet on a stage]

00:11

Records for making the biggest mural.

00:14

He had some bad experiences in the past with the metric system… [Shmonet sad as he is surrounded by metric system]

00:17

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

00:23

which we can call p.

00:25

In order to submit his mural, he needs to find the equation for the area of his mural,

00:31

in terms of “p.”

00:33

He measures the length of one side as p plus 3... [Shmonet uses a tape measure]

00:37

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

00:43

Knowing that the area formula is length times width, multiplying the two will give him the [Example of the area formula]

00:49

area of the world record mural.

00:52

We can find the product between the two polynomials by splitting up the p plus 3… [polynomials highlighted in blue]

00:58

…to get p times p-squared minus 4p plus 2… plus 3 times p-squared minus 4p plus

01:06

2.

01:08

Using the distributive property we can start distributing. [Man distributing things to people]

01:11

Though p times p squared is p-cubed, plus p times negative 4 x is minus 4p squared, plus p times

01:21

2 is 2p…

01:24

…PLUS 3 times p squared is 3p squared, plus 3 times negative 4p is minus 12p plus 3 times [Math formulas]

01:36

2 is 6.

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Combining like terms, we get p cubed minus p squared minus 10 p plus 6. [Combining like terms on chalkboard]

01:45

Poor Shmonet.

01:46

It seems his paintbrush is roughly the length of a toothpick. [Shmonet crying as hand shows small paintbrush]

01:49

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

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