12X1 T08 01 binomial expansions (2010)

Binomial Theorem

Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms.

Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 11 0 x

Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 11 0 x

xx 111 1

Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 11 0 x

xx 111 1

22 1211 xxx

Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 11 0 x

xx 111 1

22 1211 xxx

32

322

23

331221

12111

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Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms. 11 0 x

xx 111 1

22 1211 xxx

32

322

23

331221

12111

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432

43232

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Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1

Blaise Pascal saw a pattern which we now know as Pascal’s Triangle

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

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dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii

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dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii

109

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dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii

109

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3210 002.0120002.045002.0101998.0

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dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii

109

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3210 002.0120002.045002.0101998.0

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Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23

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