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Level 4 Binomial Theorem.notebook
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binomial theorem!!!!!!
Ch.11 Lesson 6
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Target
Evaluation
Agenda
Purpose
TSWBAT: expand a powered binomial and find terms using the binomial theorem
Warm-Up/Homework Check:
Lesson
BAT: to be able to put sigmas to use, raise decimals to a power, find any term from the expansion of any two terms added or subtracted then raised to a power, easier way to foil.
some exercises
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a + b is a binomial
what if it is raised to a higher power than 3?
(a+b)2
(a+b)3
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Pascal's Triangleevery entry other than 1 is the sum of the 2 entries diagonally above it.
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Using Pascal's Triangle to expand binomials
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Binomial Theorem:
Ʃ arbnr( ) n nr
coefficient 1st part of term2nd part of term
exponents always add up to power
(a+b)n =
(a+b)n = ( )an+( )an1b+( )an2b2 +...+( )a1bn1+( )bn n 0
n 1
n 2
n n1
n n
n 0
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Hold Up!the fifth row of Pascal's triangle is:
1 5 10 10 5 1
5 5 5 5 5 5 0 1 2 3 4 5
What is?!
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Factorials
Is a number with an ! at the end
it means multiply every natural number before and including it.
ex.1!= 2!= 3!= 4!=
your turn: 10!=
What about: 0!=
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Choosing Notation
( )n r n! r! (nr)!
=
How to say it: n choose r
ex. ( )65
restrictions:
r < n
r,n > 0
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Examples of: ( )n r n! r! (nr)!
=
ex. ( )65 ex. ( )6
1vs
ex. ( )64 ex. ( )6
2vs
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Hold Up we got this!the fifth row of Pascal's triangle is:
1 5 10 10 5 1
5 5 5 5 5 5 0 1 2 3 4 5
What is?!
So what can we infer from this?
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example: Set up theorem, plug in, simplify
expand using the Binomial theorem (23x)5
example:
expand using Pascals triangle (2y3x)4
example: nr = one less than the term #
Find the 3rd term using Pascals triangle (2y3x)5
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(3x + 4y2)4 find the 4th term
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Fill in what you are missing from your partner, find another person and Boggle, put a checkmark next to everything that you have but your partner doesn't have
Turn to your elbow partner and Those on the left share first
Turn your note book over and fill in as much as you can in the graphic organizer, silently for the next 2 minutes
Evaluation:
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SummarizingTIME!
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1.2.
Practice! pg.603 # 16, 915