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8.4 and 8.5 Notes 7th January 2013 1 January 07, 2013 May 49:32 AM 8.4 and 8.5 The Binomial Theorem A famous pattern of numbers is called "Pascal's Triangle".
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8.4 and 8.5 Notes
7th January 2013 1
January 07, 2013
May 49:32 AM
8.4 and 8.5 The Binomial Theorem
A famous pattern of numbers is called"Pascal's Triangle".
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May 49:33 AM
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So the 5th row starts with 4C0 and ends with 4C4.Using this concept, write the numbers for the 7th rowof Pascal's Triangle, without writing the first 6 rows!
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May 49:38 AM
We will use this concept to help us expand binomialsof order higher than 2.Ex) Expand (2x + y)6
Look at the pattern as we consider the following:
(x + y)0
(x + y)1
(x + y)2
(x + y)3
(x + y)4
What do we notice about the pattern of the numerical coefficients?
We use combinations to determine the numerical coefficient.
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May 49:42 AM
Use this pattern to expand the following:
(A + B)5
How many terms does the expansion have?
Compare that to the exponent in the binomial.
Therefore (x+y)10 would expand to have how many terms?
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Let's just look at the way we would find ONE of the termsinstead of the entire expansion.
What was term 4 of this binomial.
Notice how "r" in the nCris ONE LESS than the exponent of the binomial.
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Let's look at just the 3rd term. Can we make a conclusionabout a formula to find any "general" term instead of the entire expansion:
Notice the importance of getting this right!
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Determine the 5th term of
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Determine the middle term of
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Find the term containing x14 in (2x x2)11
In the next 2 questions we have to identify the term weare looking for, before we can find it.
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Find the term containing NO x's in
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A final question to see if you understand the Binomial Theorem formula:
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HOMEWORK: Pg 743 #4,5, 6b) 7b)c) 9, 11
Supplementary Sheet next page.
