1. Binomial Expansion
L.O.
All pupils understand why binomial expansion is important
All pupils understand the pattern binomial expansion follows
All pupils can use the binomial theorem to complete expansions

2. why binomial expansion is important
Starter:
why binomial expansion is important
This topic is all about distributions (probabilities) and the binomial expansion is useful in some of these…

3. Binomial Expansion
L.O.
All pupils understand why binomial expansion is important
All pupils understand the pattern binomial expansion follows
All pupils can use the binomial theorem to complete expansions

4. pattern binomial expansion follows
Main 1:
pattern binomial expansion follows
Pascal's Triangle 1
1 1
This is the start of Pascal's triangle. It follows a pattern, do you know or can you work out the pattern?

5. Main 1:
pattern binomial expansion follows
Pascal's Triangle 1
1 1
This is the pattern and it can continue forever!
We use this to expand brackets- lets see how? + +

6. pattern binomial expansion follows
Main 1:
pattern binomial expansion follows
Expand these:
1. (a+b)0
2. (a+b)1
3. (a+b)2
4. (a+b)3
5. (a+b)4

7. pattern binomial expansion follows
Main 1:
pattern binomial expansion follows
Expand these:
1. (a+b)0
2. (a+b)1
3. (a+b)2
(a+b)3
(a+b)4 =1
=1a+1b
=1a2+2ab+1b2
=1a3+3a2b+3ab2+1b3
=1a4+4a3b+6a2b2+4ab3+1b4

8. pattern binomial expansion follows
Main 1:
pattern binomial expansion follows
Expand these: 1
1 1 1
1a+1b
1a2+2ab+1b2
1a3+3a2b+3ab2+1b3
1a4+4a3b+6a2b2+4ab3+1b4

9. pattern binomial expansion follows
Main 1:
pattern binomial expansion follows
Expand these:
Coefficients 1
1 1
Power of 0
1. (a+b)0
2. (a+b)1
3. (a+b)2
(a+b)3
(a+b)4
Power of 1
Power of 2
Power of 3
Power of 4

10. Binomial Expansion
L.O.
All pupils understand why binomial expansion is important
All pupils understand the pattern binomial expansion follows
All pupils can use the binomial theorem to complete expansions

11. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

12. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 3 so the coefficients will be:

13. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 3 so the coefficients will be:
Terms will be:
(x)3, (x)2(2y), (x)(2y)2, (2y)3

14. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 3 so the coefficients will be:
Terms will be:
(x)3, (x)2(2y), (x)(2y)2, (2y)3
x3 , 2x2y , 4xy , 8y3

15. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 3 so the coefficients will be:
Terms will be:
(x)3, (x)2(2y), (x)(2y)2, (2y)3
x3 , 2x2y , 4xy , 8y3

16. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(x+2y)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 3 so the coefficients will be:
Terms will be:
(x)3, (x)2(2y), (x)(2y)2, (2y)3
x3 , 2x2y , 4xy , 8y3
x x2y xy2 +8y3

17. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

18. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 4 so the coefficients will be:

19. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 4 so the coefficients will be:
Terms will be:
(2x)4, (2x)3(-5), (2x)2(-5)2, (2x)(-5)3 ,(-5)4

20. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 4 so the coefficients will be:
Terms will be:
(2x)4, (2x)3(-5), (2x)2(-5)2, (2x)(-5)3 ,(-5)4
16x4, -40x3 , 100x , x , 625

21. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 4 so the coefficients will be:
Terms will be:
(2x)4, (2x)3(-5), (2x)2(-5)2, (2x)(-5)3 ,(-5)4
16x4, -40x3 , 100x , x , 625
16x x x x

22. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
How is this useful?
(2x-5)4 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
Power of 4 so the coefficients will be:
Terms will be:
(2x)4, (2x)3(-5), (2x)2(-5)2, (2x)(-5)3 ,(-5)4
16x4, -40x3 , 100x , x , 625
16x x x x
Textbook Qu.s

23. Binomial Expansion
L.O.
All pupils understand why binomial expansion is important
All pupils understand the pattern binomial expansion follows
All pupils can use the binomial theorem to complete expansions

24. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

25. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be: 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

26. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

27. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

28. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

29. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3
6c2x2 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

30. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3
6c2x2
6c2=294 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4

31. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3
6c2x2
6c2=294 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
c2=49
c=+7 or -7

32. use the binomial theorem to complete expansions
Main 2:
use the binomial theorem to complete expansions
Other Questions
(2-cx)3 The coefficient of x2 is 294
Power of 3 so the coefficients will be:
Terms will be:
(2)3, (2)2(-cx), (2)(-cx)2, (cx)3
6c2x2
6c2=294 1
1 1
Power of 0
Power of 1
Power of 2
Power of 3
Power of 4
c2=49
c=+7 or -7

33. Binomial Expansion
L.O.
All pupils understand why binomial expansion is important
All pupils understand the pattern binomial expansion follows
All pupils can use the binomial theorem to complete expansions