1. www.mathsrevision.com Nat 5 Algebraic Operations Removing Single Brackets - Revision Removing Double Brackets (ax+b)(cx+d) Alternative Method FOIL – ( NOT TAUGHT) Solving More equations (x+2) 2 =x 2 +64 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Harder Double Brackets Tidying up and Cubing (x+2) 3 Exam Questions

2. 12-Nov-15 Starter Questions www.mathsrevision.com Q1.Is the following true or false (a)(-3a) x 5a = -15a (a) (-6x) x (-7y) =-42xy Q2.Are the 2 answers the same ? (a)(-3h) 2 =(b)-(3d) 2 = Nat 5 Created by Mr. Lafferty@mathsrevision.com Q3.Spilt £64 pounds into the ratio 7:9 Q4.Explain why 0.0675 is equal to 6.75 x 10 -2

3. 12-Nov-15 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to multiply out (remove) various single brackets. 1.Understand the keypoints of multiplying out an expression with a single bracket. Nat 5 Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket

4. www.mathsrevision.com Nat 5 3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket

5. www.mathsrevision.com Nat 5 Example 3 : Write down an expression for the amount indicate below in two difference ways. 3(x + 3)=3x + 9 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket x+3

6. www.mathsrevision.com Nat 5 Example 8 : Write down an expression for the amount indicate below in two difference ways. 5(y - 2)= 5y - 10 12-Nov-15 Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket y-2

7. www.mathsrevision.com Nat 5 a(b + 5) =ab + 5a Example 4 p(w - 2) =pw - 2p Example 5 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket

8. www.mathsrevision.com Nat 5 y(y - 1) =y2y2 - y Example 6 7w(w - 3) =7w 2 - 21w Example 7 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket

9. www.mathsrevision.com Nat 5 -(x + y) =-x - y Example 8 -5(a - 7) =-5a + 35 Example 9 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket

10. www.mathsrevision.com Nat 5 7 + 3(4 - y) =7 + 12 Example 10 9 - 3(8 - y) =9 - 24 Example 11 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket - 3y = 19 - 3y Tidy Up + 3y Tidy Up = -15 + 3y

11. www.mathsrevision.com Nat 5 4(m - 3) - (m + 2) =4m - 12 - m - 2 Example 12 Example 13 12-Nov-15Created by Mr. Lafferty@mathsrevision.com = 3m - 14 Tidy Up 7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets

12. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.1 Ch1 N5 TJ (page 13) www.mathsrevision.com Nat 5 Removing a Single Bracket

13. 12-Nov-15 Starter Questions www.mathsrevision.com Q1.Find the area of the shape given Nat 5 Created by Mr. Lafferty@mathsrevision.com (w – 5) 3 Q2. Is the following true -2a( b – a) = -2ab +4a Q3.Write down the two numbers that multiply to give 8 and subtract to give 2.

14. 12-Nov-15 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to multiply out a pair of brackets using the multiplication table method. 1.Understand the keypoints of multiplying out paired brackets. Int 2 2.Be able to multiply out paired brackets using the multiplication table method. Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets

15. www.mathsrevision.com Nat 5 Below is a floor plan of the down stairs of a house. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets y 5 y 3 y 2 + 8y + 15 Living Room Kitchen Bathroom Bedroom What is the total area of the downstairs house? y 2 5y 3y15 Tidy up !

16. www.mathsrevision.com Nat 5 Multiplication table for brackets 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets (y + 3)(y + 5)y+ 3y+ 5 Double brackets are used in AREA calculations +5y +15+3y y 2 y 2 + 8y + 15 Example 1 Tidy up !

17. www.mathsrevision.com Nat 5 Example 2 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets (2x - 1)(x + 3)2x- 1x+ 3 Be careful with the negative signs +6x -3 -x 2x 2 2x 2 + 5x - 3 Tidy up !

18. www.mathsrevision.com Nat 5 = (x + 1)(x + 1) Example 3 : (x + 1) 2 Multiply out the brackets and Simplify 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Squaring Brackets (x + 1)(x + 1)x+ 1x+ 1 + x + 1+ x x 2 x 2 + 2x + 1 Tidy up !

19. www.mathsrevision.com Nat 5 Example 4 : Find the area of the square. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Harder Brackets (2x - 3y)(2x - 3y)2x- 3y2x- 3y -6xy +9y 2 -6xy 4x 2 4x 2 - 12xy + 9y 2 (2x-3y) Tidy up !

20. www.mathsrevision.com Nat 5 Example 5 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Harder Double Brackets (x + 4)(x 2 + 3x + 2) x + 4x2x2 + 3x Just a bigger Multiplication Table +3x 2 +12x +4x 2 x 3 x 3 + 2 +2x +8 + 7x 2 + 14x+ 8 Tidy up !

21. www.mathsrevision.com Nat 5 Example 6 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets (2 - 1)(x 2 + 2x - 1) 2x - 1x2x2 + 2x Just a bigger Multiplication Table +4x 2 -2x -x 2 2x 3 2x 3 - 1 -2x +1 + 3x 2 - 4x+ 1 Tidy up !

22. www.mathsrevision.com Nat 5 Example 7 : 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Harder Brackets -1 - 1 4a 2 2a ( ( 2 1 - 1 - 1 - ( ( 1 - ( ( 1 - 1 4a 2 4a 2 - 2 1 + Tidy up !

23. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.2 Ch1 N5 TJ (page 14) www.mathsrevision.com Nat 5 Removing a Single Bracket

24. 12-Nov-15 Starter Questions www.mathsrevision.com Q1.0.00897 is in scientific notation is this statement True or False? Q2.Does (w + 2)(w + 1) = w 2 + 3w + 2 Nat 5 Created by Mr. Lafferty@mathsrevision.com Q3.

25. 12-Nov-15 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to multiply out a pair of brackets using FOIL. 1.Understand the keypoints of multiplying out double brackets using FOIL. Int 2 2.Be able to multiply out double brackets using FOIL. Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets

26. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.3 Ch1 N5 TJ (page 17) www.mathsrevision.com Nat 5 Removing a Single Bracket

27. www.mathsrevision.com Nat 5 We can use the F O I L method to multiply out DOUBLE brackets. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets Simply remember the word FOIL Multiply First 2 Multiply Last 2 Multiply Outside 2 Multiply Inside 2 FOIL Method

28. www.mathsrevision.com Nat 5 (x + 1)(x + 2) x2x2 + 2x Example 1 : Multiply out the brackets and Simplify 12-Nov-15Created by Mr. Lafferty@mathsrevision.com 1.Write down F O I L + x + 2 2.Tidy up ! x 2 + 3x + 2 Removing Double Brackets Try again using multiplication table

29. www.mathsrevision.com Nat 5 (x - 1)(x + 2) x2x2 + 2x Example 2 : Multiply out the brackets and Simplify 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Removing Double Brackets 1.Write down F O I L - x - 2 2.Tidy up ! x 2 + x - 2 Try again using multiplication table

30. www.mathsrevision.com Nat 5 FOIL method is very limited therefore from now on we will use the multiplication table method. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Squaring Brackets

31. www.mathsrevision.com Nat 5 12-Nov-15Created by Mr. Lafferty@mathsrevision.com (x + 1)(x - 2) Removing Double Brackets (x - 1)(x - 2) (x + 3)(x + 2) (x - 3)(x + 2) (x + 3)(x - 2) x 2 - x - 2 x 2 - 3x + 2 x 2 + 5x + 6 x 2 - x - 6 x 2 + x - 6

32. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.2 Ch1 N5 TJ (page 14) www.mathsrevision.com Nat 5 Removing a Single Bracket

33. 12-Nov-15 Starter Questions www.mathsrevision.com Q1.Does (x - 4) 2 = x 2 + 8x + 16 Q2.3 + (-4) x 5 Nat 5 Created by Mr. Lafferty@mathsrevision.com Q3.Is it true

34. 12-Nov-15 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to expand and tidy up complicated expressions that include squared and cubed brackets. 1.Use techniques learned so far to simplify complicated brackets. Nat 5 Created by Mr. Lafferty@mathsrevision.com Simplifying Expressions

35. www.mathsrevision.com Nat 5 6m 2 - 7m - 3 Example 1 12-Nov-15Created by Mr. Lafferty@mathsrevision.com ( m 2 – 2m + 1 ) Simplifying Expressions Use multiplication table to remove brackets. Tidy up - 6m 2 - 7m - 3 - m 2 + 2m – 1 5m 2 – 5m - 4 YOU need to be VERY CAREFUL !! (2m - 3)(3m + 1) – (m - 1) 2

36. www.mathsrevision.com Nat 5 (5y – 2) 3 (25y 2 – 20y + 4) Example 1 12-Nov-15Created by Mr. Lafferty@mathsrevision.com ( 5y – 2) Simplifying Expressions Use multiplication table for first two brackets. 125y 3 – 150y 2 + 60y - 8 (5y – 2)(5y – 2)(5y – 2) Use multiplication table again

37. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.3 Ch1 N5 TJ (page 17) www.mathsrevision.com Nat 5 Simplifying Expressions

38. 12-Nov-15 Starter Questions www.mathsrevision.com Q1.Does (x + 3) 2 = x 2 + 9 Q2.The sun is 92 million mile away from the earth. Write this in standard form. Nat 5 Created by Mr. Lafferty@mathsrevision.com Q3.Is it true

39. 12-Nov-15 www.mathsrevision.com Learning Intention Success Criteria 1.We are learning how to solve equations that have paired or squared brackets. 1.Be able to solve equations that contain paired or squared brackets using multiplication table and balancing method. Nat 5 Created by Mr. Lafferty@mathsrevision.com Equations and brackets

40. www.mathsrevision.com Nat 5 m(m + 4) = (m + 1)(m+2) m 2 + 4m Example 1 12-Nov-15Created by Mr. Lafferty@mathsrevision.com = m 2 + 3m + 2 Equations and brackets 4m m = 2 = 3m + 2 12 Multiplication table Balancing Method Check !

41. www.mathsrevision.com Nat 5 (x + 5) 2 = (x - 5) 2 (x + 5)(x + 5) Example 2 12-Nov-15Created by Mr. Lafferty@mathsrevision.com = (x - 5)(x - 5) Equations and brackets x 2 + 10x + 25 20x = 0 x = 0 Multiplication table = x 2 – 10x + 25 10x + 25 = -10x + 25 Balancing Method 25 Check !

42. www.mathsrevision.com Nat 5 Balancing Method A = (x + 7)(x – 2) Example 3 : The two areas are equal. Find the value of x. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com (x + 7) (x – 2) (x + 2) A = (x + 2) 2 (x + 2) 2 = (x + 7)(x - 2) x 2 + 4x + 4 x = 18 Multiplication table Equations and brackets = x 2 + 5x - 14 4x + 4= 5x - 14 4= x - 14 400 Check !

43. 12-Nov-15Created by Mr. Lafferty@mathsrevision.com Now try Ex 1.4 Ch1 N5 TJ (page 18) www.mathsrevision.com Nat 5 Equations and Brackets