Post on 23-Jun-2015
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
331
221
12111
xxx
xxxxx
xxxx
Binomial TheoremBinomial ExpansionsA binomial expression is one which contains two terms.
11 0 x
xx 111 1
22 1211 xxx
32
322
23
331
221
12111
xxx
xxxxx
xxxx
432
43232
324
4641
33331
33111
xxxx
xxxxxxx
xxxxx
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
32
1..
xige
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
2187128
729448
243672
81560
27280
984
314
1765432 xxxxxxx
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
2187128
729448
243672
81560
27280
984
314
1765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
2187128
729448
243672
81560
27280
984
314
1765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
2187128
729448
243672
81560
27280
984
314
1765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
3210 002.0120002.045002.0101998.0
7
32
1..
xige
76
52
43
34
2567
32
32
17
32
1213
2135
32
1353
2121
32
171
xx
xxxxx
2187128
729448
243672
81560
27280
984
314
1765432 xxxxxxx
dps 8 to0.998 of value thefind to1 ofexpansion the Use 1010xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
3210 002.0120002.045002.0101998.0
98017904.0
42 5432in oft coefficien theFind xxxiii
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
xx
42 5432in oft coefficien theFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462 oft coefficien 3222 x
42 5432in oft coefficien theFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462 oft coefficien 3222 x
960
38404800
42 5432in oft coefficien theFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462 oft coefficien 3222 x
Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23
960
38404800