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Algebra www.mathsrevision.com S4 Removing Brackets & Simplifying Factors Simple Factorising 13-May-17 Created by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. A TV has be reduced in the sale by 20%. It was £250. How much is it now. 2. 5% of 300p 3. Tidy up the expression 5y + 3d + 4d + 10y 4. 2cm 3cm 6cm Find the area and perimeter of the shape. 13-May-17 Created by Mr. Lafferty Maths Dept. 2cm Algebra Removing Brackets & Simplifying www.mathsrevision.com S4 Learning Intention 1. Explain how to remove brackets and simplify. Success Criteria 1. Understand how to remove brackets 2. Apply rules integer numbers. 3. Tidy up after removing brackets. 13-May-17 Created by Mr. Lafferty Maths Dept. Removing a Single Bracket S4 www.mathsrevision.com Example 1 3(b + 5) = 3b + 15 Example 2 4(w - 2) = 4w - 8 13-May-17 Created by Mr. [email protected] Removing a Be careful with Single Bracketnegatives !! S4 www.mathsrevision.com Example 3 -2(h + 5) = -2h - 10 Example 4 -(g - 9) = -g + 9 13-May-17 Created by Mr. [email protected] Removing a Single Bracket Be careful only multiply everything inside the bracket www.mathsrevision.com S4 Example 4 8 +2(h + 3) = 8 + 2h + 6 Now tidy up ! = 2h + 14 13-May-17 Created by Mr. [email protected] Removing a Single Bracket Be careful only multiply everything inside the bracket www.mathsrevision.com S4 Example 5 -2(y - 1) + 4 = -2y + 2 + 4 Now tidy up ! = -2y + 6 13-May-17 Created by Mr. [email protected] Removing a Single Bracket Be careful only multiply everything inside the bracket www.mathsrevision.com S4 Example 6 y - (4 - y) = y - 4 + y Now tidy up ! = 2y - 4 13-May-17 Created by Mr. [email protected] Removing a Single Bracket S4 www.mathsrevision.com Example 7 a(y - 1) = ay - a Example 8 p(w - 6) = pw - 6p 13-May-17 Created by Mr. [email protected] Removing a Single Bracket S4 www.mathsrevision.com Example 9 x(x + 3) = x2 + 3x Example 10 3q(3q -2m) = 9q2 - 6mq 13-May-17 Created by Mr. [email protected] Algebra Removing Brackets & Simplifying www.mathsrevision.com S4 Now try Ex 1 Ch15 (page 172) 13-May-17 Created by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com Q1. Multiply out (a) a (6h – 3x) Q2. True or false 5 1 4 1 1 6 3 3 3 Q3. Write down all the number that divide into 12 without leaving a remainder. 13-May-17 Created by Mr. [email protected] Factors Using Factors www.mathsrevision.com S4 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-May-17 Success Criteria 1. To identify factors using factor pairs 2. Find HCF for two numbers by comparing factors. Created by Mr. [email protected] Factors Factors www.mathsrevision.com S4 Example : Find the factors of 56. Numbers that divide into 56 without leaving a remainder F56 = 1 and 56 2 and 28 4 and 14 7 and 13-May-17 8 Created by Mr. [email protected] Factors Highest Common Factor www.mathsrevision.com S4 Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. 13-May-17 Created by Mr. [email protected] Factors Highest Common Factor www.mathsrevision.com S4 Example :Find the HCF of 8 and 12. F8 = 1 and 8 F12 = 2 and 4 1 and 12 2 and 6 3 and 4 HCF = 4 13-May-17 Created by Mr. [email protected] Factors Highest Common Factor www.mathsrevision.com S4 Example : F ab = Find the HCF of ab and 2b. 1 and ab F2b = a and b 1 and 2b 2 and HCF = b b Factors Highest Common Factor www.mathsrevision.com S4 Example : Find the HCF of 4x and x2. F4x = 1, and 4x 2 and 2x 4 and Example : Fx2 = 1 and x2 x and x x HCF = x Find the HCF of 5 and 10x. F5 = 1 and 5 13-May-17 F10x = 1, and 10x 2 and 5x HCF = 5 5 and 2x Created by Mr. [email protected] 10 and x Factors www.mathsrevision.com S4 Find the HCF for these terms (a) 16w and 24w 8w (b) 9y2 and 6y 3y (c) 4h and 12h2 4h (d) ab2 and a2b ab 13-May-17 Created by Mr. [email protected] Factors www.mathsrevision.com S4 Now try Ex 2 Ch15 (page 173) 13-May-17 Created by Mr. Lafferty Starter Questions S4 www.mathsrevision.com Q1. Expand out a (4y – 3x) -2y Q2. Write out in full 4.85 10 3 Q3. True or False all the factors of 5x2 are 1, x, 5 13-May-17 Created by Mr. [email protected] Factorising Using Factors www.mathsrevision.com S4 Learning Intention 1. To show how to factorise terms using the Highest Common Factor and one bracket term. 13-May-17 Success Criteria 1. To identify the HCF for given terms. 2. Factorise terms using the HCF and one bracket term. Created by Mr. [email protected] Check by multiplying Factorising S4 www.mathsrevision.com Example out the bracket to get back to where you Factorise 3x +started 15 1. Find the HCF for 3x and 15 2. HCF goes outside the bracket 3. To see what goes inside the bracket divide each term by HCF 3x ÷ 3 = x 13-May-17 15 ÷ 3 = 5 Created by Mr. [email protected] 3 3( ) 3( x + 5 ) Check by multiplying Factorising out the bracket to get back to where you 2 started S4 www.mathsrevision.com Example Factorise 2x – 4xy + 6 1. Find the HCF for 2x2, 4xy and 6 2. HCF goes outside the bracket 3. To see what goes inside the bracket divide each term by HCF 2x2 ÷ 2 = x2 6÷2=3 4xy ÷ 2 = 2xy 13-May-17 2( 2 ) 2(x2- 2xy +3) Created by Mr. [email protected] Factorising S4 www.mathsrevision.com Factorise the following : (a) (b) 4xy – 2x (c) 6a + 7a2 (d) xy2 13-May-17 3(x + 2) 3x + 6 Be careful ! 2x(2y – 1) a(6 + 7a) -xy + 4x x(y2 – y + 4) Created by Mr. [email protected] Factorising www.mathsrevision.com S4 Now try Ex 3 Ch15 (page 175) 13-May-17 Created by Mr. [email protected]