11.6 Binomial Theorem

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11.6 Binomial Theorem
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• (a b)0 1
• (a b)1 a b
• (a b)2 a2 2ab b2
• (a b)3 a3 3a2b 3ab2 b3

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Pascals Triangle

• Coefficients for the expansion of (a b)n
• 1
• 1 1
• 1 2 1
• 1 3 3 1
• 1 4 6 4 1

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• Exponents of a begin at n and decrease
• Exponents of b begin at 0 and increase
• There are n1 terms
• Exponents of a and b n

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EX 1

• Expand (a b)4

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EX 2

• Expand (2 3x)5

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Binomial Theorem

• To expand (a b)n
• nC0an nC1an-1b nC2an-2b2 nCn-1abn-1
  nCnbn

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EX 3

• Expand

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EX 4

• Find the term with b11 in (a b)17

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EX 5

• Find the term containing x4 in (3x y)15

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EX 6

• Find the term with r18 in (r3 2s)10

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EX 7

• Find the 8th term in (a b)12

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EX8

• Find the 2nd term in (4r s2)3

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Find the coefficient of x6 in