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Match the expressions Some of the expressions below are the same. Match up the ones that are equal then write the others in a way similar to the others. 4(y – 2) 3(y + 4) y(y + 2) 2y(y – 2) y(4 – 2y) 4y – 2y² 10 – 5y 4y – 8 2y² - 4y y² + 2y

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Answers 4(y – 2) 3(y + 4) y(y + 2) 2y(y – 2) y(4 – 2y) 4y – 2y² 10 – 5y 4y – 8 2y² - 4y y² + 2y 3y (2 – y)

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Factorising Expressions Learning outcomes All – To be able to factorise simple expressions with common integer factors Most – To be able to factorise an expression into one pair of brackets Some – To be able to factorise quadratic expressions

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An example To factorise an expression we write it using brackets and take out all the common factors. Examples 1. 12a Find the highest common factor of the numbers 2.Look for any common unknown factors 3.Write the common factors outside the brackets 4.Write what is left inside the brackets (Rembering the operation +/-) What is the largest factor of 12 and 16? 4 4 x 34 x 4 Now add any unknowns x a Common factors? So 12a – 16 =4 ( ) – 3a4

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Example 2 Remember to follow each step. Examples 2. 15ab b 1.Find the highest common factor of the numbers 2.Look for any common unknown factors 3.Write the common factors outside the brackets 4.Write what is left inside the brackets (Rembering the operation +/-) What is the largest factor of 15 and 10? 5 5 x 35 x 2 Now add any unknowns x a x b x b Common factors? So 15ab b =5b ( ) + 3ab2 x b

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Questions Factorise the following expressions 1. 3x – b 3. 12c – 18c xy + 16x – 35x

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Task 2 Intermediate GCSE book Page 228 Ex 19.6Start with Q2

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Factorising Quadratics Aim – For students to be able to factorise simple quadratics where the coefficient of x 2 =1 Level – GCSE grade B

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Recap Simplify the expression (x + a)(x + b) (x + a)(x + b) F – First O – Outside I – Inside L – Last Note – use FOIL x × x = x 2 x × b = bx a × x = ax a × b = ab x2x2 + bx+ ax+ ab= x 2 + (a + b)x + ab

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So … (x + a)(x + b) = x 2 + (a + b)x + ab This is useful when factorising quadratics because… The coefficient of x is ‘a + b’ The numberical part is ‘a × b’ Example – Factorise x 2 + 7x + 12 You are looking for two numbers a and b s.t. a + b = 7 and ab = = 7 but 1 × 6 = 6 – No good = 7 and 3 × 4 = 12 – Great! Let a = 3 and b = 4 So x 2 + 7x + 12 = (x + 3)(x + 4)

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More difficult! Example Factorise x 2 – 4x – 5 You are looking for two numbers a and b s.t. a + b = -4 and ab = = -4 but 2 × -6 = -12 – No good = -4 and 1 × -5 = -5 – Great! Let a = 1 and b = -5 Therefore x 2 – 4x – 5 = (x + 1)(x – 5) Note – If their product is negative one must be negative

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Task Factorise each of the following expressions 1. x 2 + 4x x 2 + 8x x 2 + 9x x 2 – 3x – 4 5. x 2 – 7x – x 2 + 4x – x 2 – 5x + 6

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Answers 1. x 2 + 4x + 3 = (x + 1)(x + 3) 2. x 2 + 8x + 15 = (x + 3)(x + 5) 3. x 2 + 9x + 20 = (x + 4)(x + 5) 4. x 2 – 3x – 4 = (x – 4)(x + 1) 5. x 2 – 7x – 30 = (x – 10)(x + 3) 6. x 2 + 4x – 12 = (x – 2)(x + 6) 7. x 2 – 5x + 6 = (x – 2)(x – 3)

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