Created by Mr. Lafferty Maths Dept. Algebra S4 Removing Brackets & Simplifying Factors www.mathsrevision.com Simple Factorising 14-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 2cm 3cm 6cm 2cm 14-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. 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. 14-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket Example 1 3(b + 5) = 3b + 15 Example 2 4(w - 2) = 4w - 8 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Removing a Single Bracket Be careful with negatives !! Removing a Single Bracket Example 3 -2(h + 5) = -2h - 10 Example 4 -(g - 9) = -g + 9 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Removing a Single Bracket 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Removing a Single Bracket 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Removing a Single Bracket 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket Example 7 a(y - 1) = ay - a Example 8 p(w - 6) = pw - 6p 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket Example 9 x(x + 3) = x2 + 3x Example 10 3q(3q -2m) = 9q2 - 6mq 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty Maths Dept. Algebra Removing Brackets & Simplifying S4 Now try Ex 1 Ch15 (page 172) www.mathsrevision.com 14-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty@mathsrevision.com Starter Questions S4 Q1. Multiply out (a) a (6h – 3x) Q2. True or false www.mathsrevision.com Q3. Write down all the number that divide into 12 without leaving a remainder. 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com Factors Using Factors S4 Learning Intention Success Criteria To explain that a factor divides into a number without leaving a remainder To explain how to find Highest Common Factors To identify factors using factor pairs Find HCF for two numbers by comparing factors. www.mathsrevision.com 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Factors 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. 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Factors F ab = 1 and ab F2b = 1 and 2b a and b 2 and b HCF = b 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

Created by Mr. Lafferty@mathsrevision.com 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com 10 and x

Created by Mr. Lafferty@mathsrevision.com 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Factors Now try Ex 2 Ch15 (page 173) www.mathsrevision.com S4 14-Apr-17 Created by Mr. Lafferty

Created by Mr. Lafferty@mathsrevision.com Starter Questions S4 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 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@www.mathsrevision.com Factorising Using Factors S4 Learning Intention Success Criteria To show how to factorise terms using the Highest Common Factor and one bracket term. To identify the HCF for given terms. Factorise terms using the HCF and one bracket term. www.mathsrevision.com 14-Apr-17 Created by Mr. Lafferty@www.mathsrevision.com

Factorising Example Factorise 3x + 15 1. Find the HCF for 3x and 15 3 Check by multiplying out the bracket to get back to where you started Factorising S4 Example Factorise 3x + 15 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 ) 14-Apr-17 Created by Mr. Lafferty@www.mathsrevision.com

Factorising 2(x2- 2xy +3) Example Factorise 2x2 – 4xy + 6 Check by multiplying out the bracket to get back to where you started Factorising S4 Example Factorise 2x2 – 4xy + 6 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 4xy ÷ 2 = 2xy 2(x2- 2xy +3) 14-Apr-17 Created by Mr. Lafferty@www.mathsrevision.com

Created by Mr. Lafferty@mathsrevision.com 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) 14-Apr-17 Created by Mr. Lafferty@mathsrevision.com

Created by Mr. Lafferty@www.mathsrevision.com Factorising S4 Now try Ex 3 Ch15 (page 175) www.mathsrevision.com 14-Apr-17 Created by Mr. Lafferty@www.mathsrevision.com