Binomial Theorem.notebook

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Warm-Up:

1.

2.

(   ) (   )5  2

5  3

(  )+(  )3  0

3  1

3  2

3  3(  )+(  )+

Binomial Theorem.notebook

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Binomial Theorem.notebook

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binomial theorem

Ch.11     Lesson 6

Binomial Theorem.notebook

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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

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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

Binomial Theorem.notebook

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February 14, 2014

Using Pascal's Triangle to expand binomials

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

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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

Binomial Theorem.notebook

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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

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Evaluation:

1.2.

3.

Pg. 868  # [1­12, 21­42] do 1 skip 2