Algebra

1. Algebra Revision of Like Terms Revision of Removing Brackets www.mathsrevision.com Factorising 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 • Understand the techniques for simplifying terms. • We are learning to simplify terms. • 2. Be able too simplify algebraic expressions. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

4. Algebra Simplifying Algebraic Expressions Collecting LIKE terms - m + a 1 + 4g (NOT 5g ) www.mathsrevision.com 7 k2 (NOT 7k6) Created by Mr. Lafferty Maths Dept.

5. Algebra Simplifying Algebraic Expressions Multiplying Terms 6 d 4 h www.mathsrevision.com e2 (NOT 2e ) a2 8 (NOT 8a) Created by Mr. Lafferty Maths Dept.

6. Algebra Simplifying Algebraic Expressions Dividing Terms 4 www.mathsrevision.com e 3 Created by Mr. Lafferty Maths Dept.

7. Algebra Removing Brackets Now try TJN4+ Ex 5.1 Ch5 (page 31) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

8. Starter Questions 100o 60o 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 and simplifying. • 1. We are learning how to multiply out simply algebraic brackets and collecting like terms. • 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 Example + 15 3(b + 5) = 3b Example www.mathsrevision.com - 8 4(w - 2) = 4w Created by Mr. Lafferty@mathsrevision.com

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

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

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

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

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

16. Removing a Single Bracket Example 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

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

18. Removing a Single Bracket Example : 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

19. Removing Two Single Brackets Example : 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

20. Removing Two Single Brackets Example : 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

21. Algebra 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.

22. Algebra Removing Brackets Now try TJN4+ Ex 5.2 Ch5 (page 32) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

23. Starter Questions Q1. Expand out a (4y – 3x) -2y Q2. Write out in full www.mathsrevision.com Q3. True or False all the factors of 5x2 are 1, x, 5 Created by Mr. Lafferty@mathsrevision.com

24. Factorising Using Factors Learning Intention Success Criteria • To identify the HCF for given terms. • To show how to factorise terms using the Highest Common Factor and one bracket term. • Factorise terms using the HCF and one bracket term. www.mathsrevision.com Created by Mr. Lafferty@www.mathsrevision.com

25. Check by multiplying out the bracket to get back to where you started Factorising 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 3x ÷ 3 = x 15 ÷ 3 = 5 3( x + 5 ) Created by Mr. Lafferty@www.mathsrevision.com

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

27. Factorising Factorise the following : 3x + 6 4xy – 2x 3( ) x + 2 2x( ) 2y - 1 www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

28. Factorising Factorise the following : 6a + 18a2 pq– pr q - r 6a( ) 1 + 3a p( ) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

29. Factorising Factorise the following : 6xy – 8xz + 2x 3p2– 12pb p – 4b 2x( ) 3y – 4z + 1 3p( ) www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

30. Algebra Removing Brackets Now try TJN4+ Ex 5.3 Ch5 (page 33) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.