12 x1 t08 01 binomial expansions (2012)
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Transcript of 12 x1 t08 01 binomial expansions (2012)
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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xxxx
432
43232
324
464133331
33111
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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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2187128
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dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
7
321..
xige
76
52
43
34
2567
32
3217
32121
32135
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32171
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2187128
729448
243672
81560
27280
984
3141
765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
1045120210252210120451011
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7
321..
xige
76
52
43
34
2567
32
3217
32121
32135
32135
32121
32171
xx
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2187128
729448
243672
81560
27280
984
3141
765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
1045120210252210120451011
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3210 002.0120002.045002.0101998.0
7
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76
52
43
34
2567
32
3217
32121
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32121
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xx
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2187128
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81560
27280
984
3141
765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
1045120210252210120451011
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3210 002.0120002.045002.0101998.0
98017904.0
42 5432in oft coefficien theFind xxxiii
42 5432in oft coefficien theFind xxxiii 432234
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5432
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42 5432in oft coefficien theFind xxxiii 432234
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5432
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42 5432in oft coefficien theFind xxxiii 432234
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5432
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42 5432in oft coefficien theFind xxxiii 432234
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5432
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54435462 oft coefficien 3222 x
42 5432in oft coefficien theFind xxxiii 432234
4
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54435462 oft coefficien 3222 x
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42 5432in oft coefficien theFind xxxiii 432234
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54435462 oft coefficien 3222 x
Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23
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