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

7

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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

876543210

1045120210252210120451011

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

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3210 002.0120002.045002.0101998.0

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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

96038404800