Algebra www mathsrevision com S 4 Removing Brackets

Algebra www. mathsrevision. com S 4 Removing Brackets & Simplifying Factors Simple Factorising 13 -Sep-21 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 4 2 cm 3 cm 6 cm 13 -Sep-21 Created by Mr. Lafferty Maths Dept. 2 cm

Algebra Removing Brackets & Simplifying www. mathsrevision. com S 4 Learning Intention Success Criteria 1. Explain how to remove brackets and simplify. 1. Understand how to remove brackets 2. Apply rules integer numbers. 3. Tidy up after removing brackets. 13 -Sep-21 Created by Mr. Lafferty Maths Dept.

Removing a Single Bracket S 4 www. mathsrevision. com Example 1 3(b + 5) = 3 b + 15 Example 2 4(w - 2) = 4 w - 8 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Be careful with Single Bracket negatives !! S 4 www. mathsrevision. com Example 3 -2(h + 5) = -2 h - 10 Example 4 -(g - 9) = -g + 9 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Single Bracket Be careful only multiply everything inside the bracket www. mathsrevision. com S 4 Example 4 8 +2(h + 3) = 8 + 2 h + 6 Now tidy up ! = 2 h + 14 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Single Bracket Be careful only multiply everything inside the bracket www. mathsrevision. com S 4 Example 5 -2(y - 1) + 4 = -2 y + 2 + 4 Now tidy up ! = -2 y + 6 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Single Bracket Be careful only multiply everything inside the bracket www. mathsrevision. com S 4 Example 6 y - (4 - y) = y - 4 + y Now tidy up ! = 2 y - 4 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Single Bracket S 4 www. mathsrevision. com Example 7 a(y - 1) = ay - a Example 8 p(w - 6) = pw - 6 p 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Removing a Single Bracket S 4 www. mathsrevision. com Example 9 x(x + 3) = x 2 + 3 x Example 10 3 q(3 q -2 m) = 9 q 2 - 6 mq 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Algebra Removing Brackets & Simplifying www. mathsrevision. com S 4 Now try Ex 1 Ch 15 (page 172) 13 -Sep-21 Created by Mr. Lafferty Maths Dept.

Starter Questions S 4 www. mathsrevision. com Q 1. Multiply out (a) a (6 h – 3 x) Q 2. True or false Q 3. Write down all the number that divide into 12 without leaving a remainder. 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Factors Using Factors www. mathsrevision. com S 4 Learning Intention 1. To explain that a factor divides into a number without leaving a remainder 2. To explain how to find Highest Common Factors 13 -Sep-21 Success Criteria 1. To identify factors using factor pairs 2. Find HCF for two numbers by comparing factors. Created by Mr. Lafferty@mathsrevision. com

Factors www. mathsrevision. com S 4 Example : Find the factors of 56. Numbers that divide into 56 without leaving a remainder F 56 = 1 and 56 2 and 28 4 and 14 7 and 13 -Sep-21 8 Created by Mr. Lafferty@mathsrevision. com

Factors Highest Common Factor www. mathsrevision. com S 4 Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Factors Highest Common Factor www. mathsrevision. com S 4 Example : Find the HCF of 8 and 12. F 8 = 1 and 8 F 12 = 2 and 4 1 and 12 2 and 6 3 and 4 HCF = 4 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Factors Highest Common Factor www. mathsrevision. com S 4 Example : F ab = Find the HCF of ab and 2 b. 1 and ab F 2 b = a and b 1 and 2 b 2 and HCF = b b

Factors Highest Common Factor www. mathsrevision. com S 4 Example : Find the HCF of 4 x and x 2. F 4 x = 1, and 4 x Fx 2 = 1 and x 2 2 and 2 x 4 and Example : x and x x HCF = x Find the HCF of 5 and 10 x. F 5 = 1 and 5 13 -Sep-21 F 10 x = 1, and 10 x 2 and 5 x HCF = 5 5 and 2 x Created by Mr. Lafferty@mathsrevision. com 10 and x

Factors www. mathsrevision. com S 4 Find the HCF for these terms (a) 16 w and 24 w 8 w (b) 9 y 2 and 6 y 3 y (c) 4 h and 12 h 2 4 h (d) ab 2 and a 2 b ab 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Factors www. mathsrevision. com S 4 Now try Ex 2 Ch 15 (page 173) 13 -Sep-21 Created by Mr. Lafferty

Starter Questions S 4 www. mathsrevision. com Q 1. Expand out a (4 y – 3 x) -2 y Q 2. Write out in full Q 3. True or False all the factors of 5 x 2 are 1, x, 5 13 -Sep-21 Created by Mr. Lafferty@mathsrevision. com

Factorising Using Factors www. mathsrevision. com S 4 Learning Intention 1. To show to factorise terms using the Highest Common Factor and one bracket term. 13 -Sep-21 Success Criteria 1. To identify the HCF for given terms. 2. Factorise terms using the HCF and one bracket term. Created by Mr. Lafferty@www. mathsrevision. com

Check by multiplying Factorising S 4 www. mathsrevision. com Example out the bracket to get back to where you Factorise 3 x +started 15 1. Find the HCF for 3 x and 15 2. HCF goes outside the bracket 3. To see what goes inside the bracket divide each term by HCF 3 x ÷ 3 = x 13 -Sep-21 15 ÷ 3 = 5 Created by Mr. Lafferty@www. mathsrevision. com 3 3( ) 3( x + 5 )

Check by multiplying Factorising out the bracket to get back to where you 2 started S 4 www. mathsrevision. com Example Factorise 2 x – 4 xy + 6 1. Find the HCF for 2 x 2, 4 xy and 6 2. HCF goes outside the bracket 3. To see what goes inside the bracket divide each term by HCF 2 x 2 ÷ 2 = x 2 6÷ 2=3 4 xy ÷ 2 = 2 xy 13 -Sep-21 2( 2 ) 2(x 2 - 2 xy +3) Created by Mr. Lafferty@www. mathsrevision. com

Factorising S 4 www. mathsrevision. com Factorise the following : (a) (b) 4 xy – 2 x (c) 6 a + 7 a 2 (d) xy 2 13 -Sep-21 3(x + 2) 3 x + 6 Be careful ! 2 x(2 y – 1) a(6 + 7 a) -xy + 4 x x(y 2 – y + 4) Created by Mr. Lafferty@mathsrevision. com

Factorising www. mathsrevision. com S 4 Now try Ex 3 Ch 15 (page 175) 13 -Sep-21 Created by Mr. Lafferty@www. mathsrevision. com