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
xxxxxxxx
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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
xxxxxxxx
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
7
321..
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7
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76
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2187128
729448
243672
81560
27280
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765432 xxxxxxx
7
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76
52
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2187128
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765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
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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7
321..
xige
76
52
43
34
2567
32
3217
32121
32135
32135
32121
32171
xx
xxxxx
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
321..
xige
76
52
43
34
2567
32
3217
32121
32135
32135
32121
32171
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
4
5544546544432
5432
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xx
42 5432in oft coefficien theFind xxxiii 432234
4
5544546544432
5432
xxxxx
xx
42 5432in oft coefficien theFind xxxiii 432234
4
5544546544432
5432
xxxxx
xx
42 5432in oft coefficien theFind xxxiii 432234
4
5544546544432
5432
xxxxx
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54435462 oft coefficien 3222 x
42 5432in oft coefficien theFind xxxiii 432234
4
5544546544432
5432
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54435462 oft coefficien 3222 x
96038404800
42 5432in oft coefficien theFind xxxiii 432234
4
5544546544432
5432
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54435462 oft coefficien 3222 x
Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23
96038404800