what does factorial mean? for example, what is 5 factorial (5!)?

What does What does Factorial mean? Factorial mean? For ex ample, For ex ample, what is 5 what is 5 factorial (5!)? factorial (5!)?

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What does What does Factorial mean?

Factorial mean?For example,

For example, what is 5 what is 5 factorial (5!)?

factorial (5!)?

Bin

omia

l The

orem

Bin

omia

l The

orem

End In MindEnd In Mind””

Expand: (2x-7)

Expand: (2x-7)44

Page 3: What does Factorial mean? For example, what is 5 factorial (5!)?

The expression a + b is a binomial, the binomial theorem allows us to expand a binomial raised to any power.

We begin with Pascal’s Triangle

Do you notice the pattern? Can you add the next line?

Page 4: What does Factorial mean? For example, what is 5 factorial (5!)?

Binomial TheoremBinomial Theorem

11 1x y x y

2 2 21 2 1x y x xy y

3 3 2 2 31 3 3 1x y x x y xy y 4 4 3 2 2 3 41 4 6 4 1x y x x y x y xy y

01x y

What patterns do you notice?Could you write a pattern for (x+y)5

Page 5: What does Factorial mean? For example, what is 5 factorial (5!)?

App

licat

ions

App

licat

ions

7x y

52x

62 3x y

44 2x

*Do under Document Camera*

Page 6: What does Factorial mean? For example, what is 5 factorial (5!)?

Now

try:

Now

try: End In Mind

End In Mind””

Expand: (2x-7)

Expand: (2x-7)44

*Do under Document Camera*

Page 7: What does Factorial mean? For example, what is 5 factorial (5!)?

The general term

1 2 2 ...0 1 2

n n n n nn n n na b a a b a b b

*Do under Document Camera*

Finding a particular term from a binomial expansion Finding a particular term from a binomial expansion

n= the binomial’s exponentr= b’s exponent (one less than the term you’re on)

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