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Binomial Theorem.notebook
1
February 14, 2014
Warm-Up:
1.
2.
( ) ( )5 2
5 3
( )+( )3 0
3 1
3 2
3 3( )+( )+
Binomial Theorem.notebook
4
February 14, 2014
Target
Agenda
Purpose
Evaluation
Agenda
Purpose
Evaluation
TSWBAT: use the Binomial Theorem to expand powered factors and find coefficients and terms
Warm-Up/Reflection
Lesson
BAT: find any term from the expansion of any two terms added or subtracted then raised to a power, easier way to foil.
3-2-1
Binomial Theorem.notebook
5
February 14, 2014
a + b is a binomial
what if it is raised to a higher power than 3?
(a+b)2
(a+b)3
Binomial Theorem.notebook
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February 14, 2014
Pascal's Triangleevery entry other than 1 is the sum of the 2 entries diagonally above it.
Binomial Theorem.notebook
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February 14, 2014
example:
expand using Pascals triangle (23x)5
example:
expand using Pascals triangle (2y3x)4
example:
Find the 3rd term using Pascals triangle (2y3x)5
Binomial Theorem.notebook
10
February 14, 2014
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
Binomial Theorem.notebook
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February 14, 2014
Finding a Term of an expanded Binomial
(a+b)n:
arbnr( ) n nr
(2x + y )20: what is the term that contains x7
(x2 + 1/x )7: what is the coefficient of x11