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Binomial Theorem Expansion Formula
- 6. Binomial TheoremBinomial Expansions
A 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
- 7. Binomial TheoremBinomial Expansions
A 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
- 12. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
- 13. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
- 14. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
- 15. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
- 16. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
- 17. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
- 18. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
- 19. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
- 21.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
- 22.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
2187
128
729
448
243
672
81
560
27
280
9
84
3
14
1
765432
xxxxxxx
- 23.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
2187
128
729
448
243
672
81
560
27
280
9
84
3
14
1
765432
xxxxxxx
dps8to0.998ofvaluethefindto1ofexpansiontheUse
1010
xii
- 24.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
2187
128
729
448
243
672
81
560
27
280
9
84
3
14
1
765432
xxxxxxx
dps8to0.998ofvaluethefindto1ofexpansiontheUse
1010
xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
- 25.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
2187
128
729
448
243
672
81
560
27
280
9
84
3
14
1
765432
xxxxxxx
dps8to0.998ofvaluethefindto1ofexpansiontheUse
1010
xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
3210
002.0120002.045002.0101998.0
- 26.
7
3
2
1..
x
ige
76
5
2
4
3
3
4
2
567
3
2
3
2
17
3
2
121
3
2
135
3
2
135
3
2
121
3
2
171
xx
xxxxx
2187
128
729
448
243
672
81
560
27
280
9
84
3
14
1
765432
xxxxxxx
dps8to0.998ofvaluethefindto1ofexpansiontheUse
1010
xii
109
876543210
10
45120210252210120451011
xx
xxxxxxxxx
3210
002.0120002.045002.0101998.0
98017904.0
- 27. 42
5432inoftcoefficientheFind xxxiii
- 28. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
- 29. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
- 30. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
- 31. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462oftcoefficien
3222
x
- 32. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462oftcoefficien
3222
x
960
38404800
- 33. 42
5432inoftcoefficientheFind xxxiii
432234
4
5544546544432
5432
xxxxx
xx
54435462oftcoefficien
3222
x
Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23
960
38404800