Algebra

1. Algebra Simplifying Algebraic Expressions Removing Brackets Removing Brackets & Simplifying www.mathsrevision.com Evaluating Expressions Factorising – The common factor Created by Mr. Lafferty Maths Dept.

2. Starter Questions www.mathsrevision.com 2cm 3cm 6cm 2cm Created by Mr. Lafferty Maths Dept.

3. Algebra Simplifying Algebraic Expressions Learning Intention Success Criteria • To remember the phrase • ‘ like terms.’ • To review tidying up • expressions. • 2. Understand and be able too simplify simple algebraic expressions by collecting ‘ like terms.’ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

4. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

5. Rule Multiply the numbers together multiply the letters together. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Simplifying Algebraic Expressions Reminder ! Multiplying terms www.mathsrevision.com ( NOT 2b ) ( NOT 8m ) Created by Mr. Lafferty Maths Dept.

6. 1 2 3 Algebra MTH 3-14a MTH 4-14a MTH 4-14b Simplifying Algebraic Expressions Question : Find the area of each of the 3 sections of this shape. What is the total area. y www.mathsrevision.com 2 y 2 Created by Mr. Lafferty Maths Dept.

7. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Simplifying Algebraic Expressions Now try Exercise 1 Ch11 (page 46) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

8. 100o 60o Starter Questions 2a 6h www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

9. Algebra Removing brackets Learning Intention Success Criteria • Understand the key steps in removing brackets. • 1. We are learning how to multiply out simply algebraic brackets. • 2. Apply multiplication rules for positive and negative numbers when removing brackets. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

10. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 1 + 15 3(b + 5) = 3b Example 2 www.mathsrevision.com - 8 4(w - 2) = 4w Created by Mr. Lafferty@mathsrevision.com

11. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 3 - 2 2(y - 1) = 2y Example 4 www.mathsrevision.com - 42 7(w - 6) = 7w Created by Mr. Lafferty@mathsrevision.com

12. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 5 + 24 8(x + 3) = 8x Example 6 www.mathsrevision.com - 8m 4(3 -2m) = 12 Created by Mr. Lafferty@mathsrevision.com

13. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 7 : Write down an expression for the amount indicate below in two difference ways. x+3 x+3 www.mathsrevision.com + 9 3(x + 3) =3x x+3 Created by Mr. Lafferty@mathsrevision.com

14. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 8 : Write down an expression for the amount indicate below in two difference ways. y-2 y-2 y-2 www.mathsrevision.com - 10 5(y - 2) = 5y y-2 y-2 10-Mar-14 Created by Mr. Lafferty@mathsrevision.com

15. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Removing brackets Question : Find the area of the rectangle (i) With brackets (ii) Without brackets. y + 5 (i) A = L x B www.mathsrevision.com 4 = 4(y + 5) (ii) = 4(y + 5) = 4y + 20 Created by Mr. Lafferty Maths Dept.

16. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Removing brackets Now try Exercise 2 Ch11 (page 48) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

17. Starter Questions www.mathsrevision.com (x+2)cm 7cm Created by Mr. Lafferty Maths Dept.

18. Algebra Removing Brackets & Simplifying Learning Intention Success Criteria 1. Understand how to remove brackets • 1. We are learning how to remove brackets and simplify. 2. Understand the need to show clear working. www.mathsrevision.com 3. Apply to context questions. Created by Mr. Lafferty Maths Dept.

19. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 1 + 5a a(b + 5) = ab Example 2 www.mathsrevision.com - 2p p(w - 2) = pw Created by Mr. Lafferty@mathsrevision.com

20. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 3 - y y(y - 1) = y2 Example 4 www.mathsrevision.com - 21w 7w(w - 3) = 7w2 Created by Mr. Lafferty@mathsrevision.com

21. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 5 + 3ab a(a2 + 3b) = a3 Example 6 www.mathsrevision.com - 2cy2 y2(3y -2c) = 3y3 Created by Mr. Lafferty@mathsrevision.com

22. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 7 - y -(x + y) = -x Example 8 www.mathsrevision.com + 35 -5(a - 7) = -5a Created by Mr. Lafferty@mathsrevision.com

23. Removing a Single Bracket Tidy Up MTH 3-14a MTH 4-14a MTH 4-14b Example 9 - 3y 12 7 + 3(4 - y) = 7 + = 19 - 3y Tidy Up Example 10 www.mathsrevision.com - 24 + 3y 9 - 3(8 - y) = 9 = -15 + 3y Created by Mr. Lafferty@mathsrevision.com

24. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 11 12 10 Find my Area Find my Area x (x - 2) www.mathsrevision.com A = L x B A = L x B A = 10(x – 2) A = 12x Created by Mr. Lafferty@mathsrevision.com

25. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b Example 12 : Find area of the orange border 12 Area =Big Rec – Small Rec 10 x (x - 2) = 12x – 10(x - 2) www.mathsrevision.com = 12x -10x + 20 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

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

27. Removing Two Single Brackets MTH 3-14a MTH 4-14a MTH 4-14b Example 15 : Find an expression for the difference in the areas. (y - 5) A = 4(y – 5) 7 4 A = 7(y - 4) www.mathsrevision.com (y - 4) Calculate difference if y = 14 Diff = 3 x 14 – 8 = 34 Difference = 7(y - 4) - 4(y – 5) = 7y - 28 - 4y + 20 = 3y - 8 Created by Mr. Lafferty@mathsrevision.com

28. Removing Two Single Brackets MTH 3-14a MTH 4-14a MTH 4-14b Example 16 : Find an expression for the difference in the areas. (x + 1) A = 7(x + 1) 9 7 A = 9(x + 3) www.mathsrevision.com x + 3 Calculate difference if x = 4 Diff = 2 x 4 + 20 =28 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

29. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Removing Brackets & Simplifying Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section. x x-3 4 Ab= 6x 6 www.mathsrevision.com As= 4(x - 3) = 4x - 12 As= 6x - 4(x - 3) = 6x - 4x + 12 = 2x + 12 Created by Mr. Lafferty Maths Dept.

30. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Removing Brackets & Simplifying Now try Exercise 3 Ch11 (page 50) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

31. Starter Questions www.mathsrevision.com (x+2)cm 7cm Created by Mr. Lafferty Maths Dept.

32. Algebra Evaluating Expressions – number for letter Learning Intention Success Criteria 1. Be able to substitute numbers for letters in an expression. • 1. We are learning how to evaluate an expression. 2. Use previous knowledge of Number to evaluate a expression. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

33. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Evaluating Expressions – number for letter BODMAS Given the following information find the values of :- a = 3 ; b = 4 and c = -1 2a + c b2 – a2 2b2 = 42 – 32 = 2x3 + (-1) = 2x(4)2 www.mathsrevision.com = 16 – 9 = 2x3 - 1 = 2x16 = 6 - 1 = 7 = 32 = 5 Created by Mr. Lafferty Maths Dept.

34. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 2a2 + 3b + 30c = 2x(3)2 + 3x4 + 30x(-1) www.mathsrevision.com = 18 + 12 - 30 = 0 Created by Mr. Lafferty Maths Dept.

35. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Evaluating Expressions – number for letter Now try Exercise 4 Ch2 (page 51) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

36. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

37. Algebra Factorising – The Common Factor Learning Intention Success Criteria 1. Understand the term factorising. • 1. We are learning the process of factorising’. 2. Apply previous knowledge to recognise the HCF for a set of values. www.mathsrevision.com 3. Analysis answer to validate it is correct. Created by Mr. Lafferty Maths Dept.

38. Check by multiplying out the bracket to get back to where you started Factorising MTH 3-14a MTH 4-14a MTH 4-14b Factorise 3x + 15 Example 1. Find the HCF for 3x and 15 3 2. HCF goes outside the bracket 3( ) www.mathsrevision.com • To see what goes inside the bracket • divide each term by HCF 15 3x 3( x + 5 ) = x = 5 3 3 Created by Mr. Lafferty@www.mathsrevision.com

39. Check by multiplying out the bracket to get back to where you started Factorising MTH 3-14a MTH 4-14a MTH 4-14b Factorise 4x2 – 6xy Example 1. Find the HCF for 4x2 and 6xy 2x 2. HCF goes outside the bracket 2x( ) www.mathsrevision.com • To see what goes inside the bracket • divide each term by HCF 6xy 4x2 2x( 2x - 3y ) = 2x = 3y 2x 2x Created by Mr. Lafferty@www.mathsrevision.com

40. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Factorising – The Common Factor Simply find the HCF for a given set of data and write the data using brackets :- 8a – 12b 6x – 12 www.mathsrevision.com = ( ) = ( ) 4 2a - 3b 6 x - 2 Created by Mr. Lafferty Maths Dept.

41. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Factorising – The Common Factor Simply find the HCF for a given set of data and write the data using brackets :- 9f – 6f2 am + an www.mathsrevision.com = ( ) = ( ) 3f 3 - 2f a m + n Created by Mr. Lafferty Maths Dept.

42. Factorising MTH 3-14a MTH 4-14a MTH 4-14b Factorise the following : = ( ) 3 x + 2 • (a) 3x + 6 • 4xy – 2x • 6a + 7a2 • (d) y2 - y = ( ) 2x 2y - 1 www.mathsrevision.com = ( ) a 6 + 7a = ( ) y y - 1 Created by Mr. Lafferty@mathsrevision.com

43. Algebra MTH 3-14a MTH 4-14a MTH 4-14b Factorising – The Common Factor Now try Exercise 5 Ch11 (page 54) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.