what does factorial mean? for example, what is 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!)?
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Bin
omia
l The
orem
Bin
omia
l The
orem
End In MindEnd In Mind””
Expand: (2x-7)
Expand: (2x-7)44
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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?
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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
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App
licat
ions
App
licat
ions
7x y
52x
62 3x y
44 2x
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Now
try:
Now
try: End In Mind
End In Mind””
Expand: (2x-7)
Expand: (2x-7)44
*Do under Document Camera*
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The general term
The general term
1 2 2 ...0 1 2
n n n n nn n n na b a a b a b b
n
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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)