1. Expanding and Simplifying Algebraic Expressions
Lesson Aims:
To be able to simplify algebraic expressions with adding, subtracting and multiplying
To be able to expand a single bracket, including negative numbers

2. Review of Algebraic Expressions
So far we have learned that: 2c means 2 multiplied by c z means z divided by six. 6

3. What is the value of this expression?
y when y = 4

4. What is the value of this expression?
y when y = 4
(4 x 4) + 5 = = 21

5. Is this true for any number. a + b = b + a (hint: does 4 + 3 = 3 + 4
Is this true for any number? a + b = b + a (hint: does = 3 + 4? Imagine that a and b are numbers. Does it matter what order we use to add them?

6. Is this true for any number. a - b = b - a (hint: does 7 - 5 = 5 - 7
Is this true for any number? a - b = b - a (hint: does = 5 - 7? Imagine that a and b are numbers. Does it matter what order we use to subtract them?

7. Simplifying Expressions
What we already know
When we have
a + a + a =
We collect them together = 3a
a + 3a – a =
1 + 3 – 1 = 3
= 3a

8. Simplifying Expressions
What we already know
a x a x a x a = similar to indices
4 x 4 x 4 x 4 = 44
So a x a x a x a = a4

9. Simplifying Expressions
2p + 4p = +

10. Simplifying Expressions
2p + 4p = So 2p + 4p = 6p +

11. Simplifying Expressions
2a + 3a = +

12. Simplifying Expressions
2a + 3a = + =
2a +3a = 5a

13. Simplifying Expressions
2a + p = +

14. Simplifying Expressions
We can only simplify when the terms have the same letter or variable. 2a + p = +
= 2a + p

15. Simplifying Expressions
2a + p + 4a + 2k + 3p =

16. Simplifying Expressions
2a + p + 4a + 2k + 3p = First look at a: Then look at p: Then look at k:

17. Simplifying Expressions
2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: Then look at k:

18. Simplifying Expressions
2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k:

19. Simplifying Expressions
2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k

20. Simplifying Expressions
2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k So the expression becomes: 6a + 4p + 2k

21. Simplifying Expressions
Try these
4f + 7b – f + 3b =
h + 3h – 2h + 2h – 3h =
8a + b – c – 7a =
3y + b + 2b – y + 8 =
4c - 2d – 2c – 3d =
extension
8d³ + 2d² - 3d² =
3s³ + 4s³ - s =

22. Simplifying Expressions
a x a x a x b x b = a3b2
a x b x c = abc
2a x b x c = 2abc
d x r x d x r =
r x r x d x d = r2d2

23. Simplifying Expressions
2a x 2b x c =
Remember with multiplying no matter what order you put the numbers your multiplying you will get the same answer.
So I will put the numbers and the letters together

24. Simplifying Expressions
2a x 2b x c =
2 x 2 x a x b x c = 4abc

25. Simplifying Expressions
s x s x s x s =
r x s x r x s x r =
4d x 3 d =
2a x 3d x 4a =
6c x 6v x 4b =
3n x 5 b x f=
Extension
3r x 3r x 3r =

26. Expanding Brackets 3(a + 5) What does this mean?
‘add five to a then multiply the whole lot by three’ Or
‘three lots of a added to three lots of 5

27. Expanding Brackets
3(a + 5)
+ 5
+ 5 a a
+ 5 a

28. Expanding Brackets
3(a + 5)
+ 5
+ 5 a a
+ 5 a
3(a + 5) =

29. Expanding Brackets
3(a + 5)
+ 5
+ 5 a a
+ 5 a
3(a + 5) = (3 x a) +

30. Expanding Brackets + 5 + 5 + 5 3(a + 5) = (3 x a) + (3 x 5) = 3(a + 5)

31. Expanding Brackets + 5 + 5 + 5 3(a + 5) = (3 x a) + (3 x 5) = 3a + 15

32. Expanding Brackets + 4 + 4 + 4 + 4 + 4 + 4 6(2a + 4) 6(2a + 4) =
(6 x 2a) + (6 x 4)
= 12a + 24

33. Expanding Brackets
Example: 5(2z – 3) Each term inside the brackets is multiplied by the number outside the brackets. Watch out for the signs!

34. Expanding Brackets
Example: 5(2z – 3) (5 x 2z) – 5 x 3

35. Expanding Brackets
Example: 5(2z – 3) (5 x 2z) – 5 x 3 = 10z – 15

36. Expanding Brackets Example t( 3 +7)
Rememeber muliplty everything inside the bracket by whats outside the bracket.
(t x 3) + (t x 7)
3t + 7t
= 10t

37. Expanding Brackets
Example
r(6m -5)
(r x 6m) – (r x 5)
6mr – 5r

38. Expanding Brackets y(2 + y) 4(y + 3) a(7 – 8) 5(a + 9) p(3p + q)
extension
4(y + 3)
5(a + 9)
3(x – 7)
6(g – 2)
2(3b + 7)
10(3k + 10)
12(4s + 6)
y(2 + y)
a(7 – 8)
p(3p + q)
s(6s – 5)
k(2m + n)

39. Expanding Brackets
When we have 2 brackets the rules are the same. Multiply what's inside the bracket be what is out of the bracket. Remember to be careful of signs. We are only going to have addition in the middle of the brackets today is minus gets tricky! Example: 2(3p + 4) + 3(4p + 1)

40. Expanding Brackets
Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4)

41. Expanding Brackets
Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)

42. Expanding Brackets
Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8

43. Expanding Brackets
Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p p + 3

44. Expanding Brackets
Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p p + 3 = 18p + 11

45. Expanding Brackets 5(x + 3) + 2(x – 7) First bracket 5x + 15
Second bracket
2x -14
simplify
5x x -14
7x +1

46. Expanding Brackets 3(x – 5) + 4(x + 6) 3(2x – 1) +2(3x + 4)