Algebra

1. S4 Algebra Removing Brackets & Simplifying Factors www.mathsrevision.com Simple Factorising Created by Mr. Lafferty Maths Dept.

2. S4 Starter Questions www.mathsrevision.com 2cm 3cm 6cm 2cm Created by Mr. Lafferty Maths Dept.

3. Algebra Removing Brackets & Simplifying S4 Learning Intention Success Criteria 1. Understand how to remove brackets • 1. Explain how to remove brackets and simplify. 2. Apply rules integer numbers. www.mathsrevision.com 3. Tidy up after removing brackets. Created by Mr. Lafferty Maths Dept.

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

5. Be careful with negatives !! Removing a Single Bracket Example 3 - 10 -2(h + 5) = -2h Example 4 + 9 -(g - 9) = -g Created by Mr. Lafferty@mathsrevision.com

6. Be careful only multiply everything inside the bracket Removing a Single Bracket Example 4 8 +2(h + 3) = 8 + 2h + 6 Now tidy up ! = 2h + 14 Created by Mr. Lafferty@mathsrevision.com

7. Be careful only multiply everything inside the bracket Removing a Single Bracket Example 5 -2(y - 1) + 4 = -2y + 2 + 4 Now tidy up ! = -2y + 6 Created by Mr. Lafferty@mathsrevision.com

8. Be careful only multiply everything inside the bracket Removing a Single Bracket Example 6 y - (4 - y) = y - 4 + y Now tidy up ! = 2y - 4 Created by Mr. Lafferty@mathsrevision.com

9. Removing a Single Bracket Example 7 - a a(y - 1) = ay Example 8 - 6p p(w - 6) = pw Created by Mr. Lafferty@mathsrevision.com

10. Removing a Single Bracket Example 9 + 3x x(x + 3) = x2 Example 10 - 6mq 3q(3q -2m) = 9q2 Created by Mr. Lafferty@mathsrevision.com

11. Algebra Removing Brackets & Simplifying S4 Now try Ex 1 Ch15 (page 172) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

12. S4 Q1. Multiply out (a) a (6h – 3x) Starter Questions Q2. True or false www.mathsrevision.com Q3. Write down all the number that divide into 12 without leaving a remainder. Created by Mr. Lafferty@mathsrevision.com

13. Factors Using Factors S4 Learning Intention Success Criteria • To identify factors using factor pairs • To explain that a factor divides into a number without leaving a remainder • To explain how to find Highest Common Factors • Find HCF for two numbers by comparing factors. www.mathsrevision.com Created by Mr. Lafferty@mathsrevision.com

14. Factors Factors S4 Example : Find the factors of 56. Numbers that divide into 56 without leaving a remainder F56 = 1 and 56 2 and 28 www.mathsrevision.com 4 and 14 7 and 8 Created by Mr. Lafferty@mathsrevision.com

15. Factors Highest Common Factor S4 Highest Common Factor Largest Same Number www.mathsrevision.com We need to write out all factor pairs in order to find the Highest Common Factor. Created by Mr. Lafferty@mathsrevision.com

16. Factors Highest Common Factor S4 Example : Find the HCF of 8 and 12. F8 = 1 and 8 2 and 4 F12 = 1 and 12 2 and 6 3 and 4 www.mathsrevision.com HCF = 4 Created by Mr. Lafferty@mathsrevision.com

17. Factors Highest Common Factor S4 Example : Find the HCF of ab and 2b. F ab = 1 and ab a and b F2b = 1 and 2b 2 and b www.mathsrevision.com HCF = b

18. Factors Highest Common Factor S4 Example : Find the HCF of 4x and x2. F4x = 1, and 4x Fx2 = 1 and x2 2 and 2x x and x 4 and x HCF = x www.mathsrevision.com Example : Find the HCF of 5 and 10x. F5 = 1 and 5 F10x = 1, and 10x 2 and 5x HCF = 5 5 and 2x Created by Mr. Lafferty@mathsrevision.com 10 and x

19. Factors S4 Find the HCF for these terms 8w • (a) 16w and 24w • 9y2 and 6y • (c) 4h and 12h2 • (d) ab2 and a2b 3y www.mathsrevision.com 4h ab Created by Mr. Lafferty@mathsrevision.com

20. Factors S4 Now try Ex 2 Ch15 (page 173) www.mathsrevision.com Created by Mr. Lafferty

21. S4 Q1. Expand out a (4y – 3x) -2y Starter Questions 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

22. Factorising Using Factors S4 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

23. Check by multiplying out the bracket to get back to where you started Factorising S4 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

24. Check by multiplying out the bracket to get back to where you started Factorising S4 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

25. Factorising S4 Factorise the following : 3(x + 2) • (a) 3x + 6 • 4xy – 2x • 6a + 7a2 • (d) xy2 -xy + 4x Be careful ! 2x(2y – 1) www.mathsrevision.com a(6 + 7a) x(y2 – y + 4) Created by Mr. Lafferty@mathsrevision.com

26. Factorising S4 Now try Ex 3 Ch15 (page 175) www.mathsrevision.com Created by Mr. Lafferty@www.mathsrevision.com