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Algebraic Operations

Algebraic Operations. Removing Brackets of the type 2(x-1). Removing Brackets of the type y(3+a). Removing Brackets of the type -2(x+1). Equations and brackets 3(x-4) = 2(x-1). Pair of brackets (x+3)(x+4). Squaring Brackets (x+4) 2. More equations (x+2) 2 =x 2 +64. S3.3.

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Algebraic Operations

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  1. Algebraic Operations Removing Brackets of the type 2(x-1) Removing Brackets of the type y(3+a) Removing Brackets of the type -2(x+1) Equations and brackets 3(x-4) = 2(x-1) Pair of brackets (x+3)(x+4) Squaring Brackets (x+4)2 More equations (x+2)2 =x2 +64 Created by Mr. Lafferty@mathsrevision.com

  2. S3.3 Q1. Is the following true or false (a) (-3a) x 5a = -15a (a) (-6x) x (-7y) =-42xy Starter Questions Q2. Are the 2 answers the same ? (a) (-3h)2 = (b) -(3d)2 = www.mathsrevision.com Q3. Spilt £64 pounds into the ratio 7:9 Q4. Explain why 0.0675 is equal to 6.75x10-2 Created by Mr. Lafferty@mathsrevision.com

  3. Removing a Single Bracket S3.3 Learning Intention Success Criteria • To show how to multiply out (remove) a single bracket with a positive number outside the bracket. • Understand the keypoints of multiplying out an expression with a single bracket and a positive number outside the bracket. www.mathsrevision.com • Be able multiply out a expression with a single bracket. Created by Mr. Lafferty@mathsrevision.com

  4. Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  5. Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms www.mathsrevision.com ( NOT 2b ) ( NOT 8m ) Created by Mr. Lafferty Maths Dept.

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

  7. Removing a Single Bracket Example 3 - 2 2(y - 1) = 2y Example 4 - 42 7(w - 6) = 7w Created by Mr. Lafferty@mathsrevision.com

  8. Removing a Single Bracket Example 5 + 24 8(x + 3) = 8x Example 6 - 8m 4(3 -2m) = 12 Created by Mr. Lafferty@mathsrevision.com

  9. Removing a Single Bracket Example 7 : Write down an expression for the amount indicate below in two difference ways. x+3 x+3 + 9 3(x + 3) =3x x+3 Created by Mr. Lafferty@mathsrevision.com

  10. Removing a Single Bracket Example 8 : Write down an expression for the amount indicate below in two difference ways. y-2 y-2 y-2 - 10 5(y - 2) = 5y y-2 y-2 8-Aug-14 Created by Mr. Lafferty@mathsrevision.com

  11. Removing a Single Bracket S3.3 Now try Ex 2.1 Ch3 MIA (page 43) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  12. S3.3 Q1. Explain why the following are True or False (a) -3y x 5y = -30y (b) -6q x (-4q) = 24q2 Starter Questions Q2. Is the following true -2a( b – a) = -2ab +4a www.mathsrevision.com Q3. Write down the two numbers that multiply to give 8 and subtract to give 2. Created by Mr. Lafferty@mathsrevision.com

  13. Removing a Single Bracket S3.3 Learning Intention Success Criteria • To show how to multiply out (remove) a single bracket with a letter outside the bracket. • Understand the keypoints of multiplying out an expression with a single bracket with a letter outside. www.mathsrevision.com • Be able multiply out a expression with a single bracket with a letter outside the bracket. Created by Mr. Lafferty@mathsrevision.com

  14. Removing a Single Bracket Example 1 + 5a a(b + 5) = ab Example 2 - 2p p(w - 2) = pw Created by Mr. Lafferty@mathsrevision.com

  15. Removing a Single Bracket Example 3 - y y(y - 1) = y2 Example 4 - 21w 7w(w - 3) = 7w2 Created by Mr. Lafferty@mathsrevision.com

  16. Removing a Single Bracket Example 5 + 3ab a(a2 + 3b) = a3 Example 6 - 2cy2 y2(3y -2c) = 3y3 Created by Mr. Lafferty@mathsrevision.com

  17. Removing a Single Bracket S3.3 Now try Ex 2.2 Ch3 MIA (page 44) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  18. S3.3 Q1. Multiply out. (a) 3y(x - y) = (b) 6q2 (2 - 4q) = Starter Questions Q2. Explain your working to show that if we split 24 into the ratio 1:5 the answer is 4:20 www.mathsrevision.com Q3. Writing out in full 5.2 x 10-3 to get 0.052 Is the correct? Created by Mr. Lafferty@mathsrevision.com

  19. Removing a Single Bracket S3.3 Learning Intention Success Criteria • To show how to multiply out (remove) a single bracket with a negative outside the bracket. • Understand the keypoints of multiplying out an expression with a single bracket with a negative outside. www.mathsrevision.com • Be able multiply out a expression with a single bracket with a negative outside the bracket. Created by Mr. Lafferty@mathsrevision.com

  20. Removing a Single Bracket Example 1 - y -(x + y) = -x Example 2 + 35 -5(a - 7) = -5a Created by Mr. Lafferty@mathsrevision.com

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

  22. Removing a Single Bracket Example 9 12 10 Find my Area Find my Area x (x - 2) A = L x B A = L x B A = 10(x – 2) A = 12x Created by Mr. Lafferty@mathsrevision.com

  23. Removing a Single Bracket Example 9 : Find area of the orange border 12 Area =Big Rec – Small Rec 10 x (x - 2) = 12x – 10(x - 2) = 12x – 10x + 20 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  24. Removing a Single Bracket S3.3 Now try Ex 3.1 Ch3 MIA (page 44) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  25. S3.3 Q1. Find the area of the second shape given the first has area 7w - 14 Starter Questions (w - 2) (w – 5) 3 7 www.mathsrevision.com Q2. Split 48 into the ratio 1:3 Q3. In standard form 18294000 is 1.8x107 is the correct? Created by Mr. Lafferty@mathsrevision.com

  26. Removing Two Single Brackets S3.3 Learning Intention Success Criteria • To show how to multiply out (remove) and simplify an expression that has two single brackets. • Understand the keypoints of multiplying out an expression with two single brackets. www.mathsrevision.com • Be able multiply out a expression with two single brackets and the simplify. Created by Mr. Lafferty@mathsrevision.com

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

  28. Removing Two Single Brackets Example 3 : Find an expression for the difference in the areas. (y - 5) A = 4(y – 5) 7 4 A = 7(y- 4) (y- 4) Calculate difference if y = 14 3 x 14 – 8 = 34 Difference = 7(y - 4) - 4(y – 5) = 7y - 28 - 4y + 20 = 3y - 8 Created by Mr. Lafferty@mathsrevision.com

  29. Removing Two Single Brackets Example 3 : Find an expression for the difference in the areas. (x + 1) A = 7(x + 1) 9 7 A = 9(x + 3) x + 3 Calculate difference if x = 4 2 x 4 + 20 =28 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  30. Removing Two Single Brackets S3.3 Now try Ex 3.2 Ch3 MIA (page 46) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  31. S3.3 Q1. Solve for x (a) x + 3 = 8 (b) 2x – 14 = 50 Starter Questions Q2. Is this statement true (x – 1) – 3(x + 1) = -2x www.mathsrevision.com Q3. Created by Mr. Lafferty@mathsrevision.com

  32. Equations and brackets S3.3 Learning Intention Success Criteria • To show how to solve equations that have bracket terms. • Be able to multiply out brackets and solve equations. www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  33. Equations and brackets Multiply out the bracket first and then solve. Example 1 25 5(x - 3) = 5x - 15 = 25 = 40 5x = 25 + 15 x = 40 ÷ 5 = 8 Created by Mr. Lafferty@mathsrevision.com

  34. Equations and brackets 18 18 Example 2 3(x + 1) 6(x - 2) = Solve as normal Substitute value into original equation to check answer = 3x + 3 - 12 6x = 3 6x – 3x -12 = 3 3x -12 = 3 + 12 3x = 15 3x = 5 = 15 ÷ (3) x Created by Mr. Lafferty@mathsrevision.com

  35. Equations and brackets 6 6 Example 3 Tidy up RHS 6 – (y + 2) -3(2 + 2y) = Substitute value into original equation to check answer - y - 2 = 6 - 6y -6 Solve as normal = 4 - y -6 – 6y = 4 -6 - 6y + y = 4 -6 – 5y = 10 – 5y = -2 = 10 ÷ (-5) y Created by Mr. Lafferty@mathsrevision.com

  36. Equations and brackets S3.3 Now try Ex 4.1 & Ex 4.2 Ch3 MIA (page 47) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  37. S3.3 Q1. Does 579300 = 5.793x105 Starter Questions Q2. Explain why the answer to 4(w + 2) = 6(w + 1) is w = 1 www.mathsrevision.com Q3. Created by Mr. Lafferty@mathsrevision.com

  38. Removing Double Brackets Int 2 Learning Intention Success Criteria • To show how to multiply out a pair of brackets using a multiplication table. • Understand the keypoints of multiplying out paired brackets. • Be able to multiply out paired brackets using a multiplication table. www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  39. What is the total area of the downstairs house? Removing Double Brackets Below is a floor plan of the down stairs of a house. y 5 Living Room y y2 5y Bedroom Tidy up ! 3y 15 3 Kitchen Bathroom y2 + 8y + 15 Created by Mr. Lafferty@mathsrevision.com

  40. Removing Double Brackets Double brackets are used in AREA calculations Multiplication table for brackets (y + 3)(y + 5) y + 3 y + 5 Tidy up ! y2 +5y +3y +15 y2 + 8y + 15 Created by Mr. Lafferty@mathsrevision.com

  41. Removing Double Brackets Be careful with the negative signs Example 2 (2x - 1)(x + 3) 2x - 1 x + 3 Tidy up ! +6x 2x2 2x2 + 5x - 3 -3 -x Created by Mr. Lafferty@mathsrevision.com

  42. Removing Double Brackets Just a bigger Multiplication Table Example 3 (x + 4)(x2 + 3x + 2) x2 + 3x + 2 x + 4 Tidy up ! +3x2 x3 +2x x3 + 7x2 + 14x + 8 +12x +8 +4x2 Created by Mr. Lafferty@mathsrevision.com

  43. Removing Double Bracket S3.3 Now try Ex 5.1 First column in each Question Ch3 MIA (page 49) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

  44. S3.3 Q1. 0.00897 is in scientific notation is this statement True or False? Starter Questions Q2. Why does (w + 2)(w + 1) = w2 + 3w + 2 www.mathsrevision.com Q3. Created by Mr. Lafferty@mathsrevision.com

  45. Removing Double Brackets Int 2 Learning Intention Success Criteria • To show how to multiply out a pair of brackets using FOIL. • Understand the keypoints of multiplying out double brackets using FOIL. • Be able to multiply out double brackets using FOIL. www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

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

  47. Removing Double Brackets Try again using multiplication table Example 1 : Multiply out the brackets and Simplify (x + 1)(x + 2) 1. Write down F O I L x2 + 2x + x + 2 x2 + 3x + 2 2. Tidy up ! Created by Mr. Lafferty@mathsrevision.com

  48. Removing Double Brackets Try again using multiplication table Example 2 : Multiply out the brackets and Simplify (x - 1)(x + 2) 1. Write down F O I L x2 + 2x - x - 2 x2 + x - 2 2. Tidy up ! Created by Mr. Lafferty@mathsrevision.com

  49. Squaring Brackets FOIL method is very limited therefore from now on we will use the multiplication table method. Created by Mr. Lafferty@mathsrevision.com

  50. Removing Double Brackets (x + 1)(x - 2) x2 - x - 2 (x - 1)(x - 2) x2 - 3x + 2 (x + 3)(x + 2) x2 + 5x + 6 (x - 3)(x + 2) x2 - x - 6 (x + 3)(x - 2) x2 + x - 6 Created by Mr. Lafferty@mathsrevision.com

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