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**Match the expressions 4(y – 2) 4y – 2y² 3(y + 4) 10 – 5y y(y + 2)**

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

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**Answers 4(y – 2) 4y – 2y² 3(y + 4) 10 – 5y y(y + 2) 4y – 8 5(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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**What is the largest factor of 12 and 16?**

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

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**What is the largest factor of 15 and 10?**

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

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**Questions Factorise the following expressions 3x – 9 10 + 4b**

12c – 18c2 20xy + 16x2 5 – 35x

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

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**Factorising Quadratics**

Aim – For students to be able to factorise simple quadratics where the coefficient of x2=1 Level – GCSE grade B

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**Simplify the expression (x + a)(x + b)**

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 = x2 x × b = bx a × x = ax a × b = ab x2 + bx + ax + ab = x2 + (a + b)x + ab

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**(x + a)(x + b) = x2 + (a + b)x + ab**

So … (x + a)(x + b) = x2 + (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 x2 + 7x + 12 You are looking for two numbers a and b s.t. a + b = 7 and ab = 12 1 + 6 = 7 but 1 × 6 = 6 – No good 3 + 4 = 7 and 3 × 4 = 12 – Great! Let a = 3 and b = 4 So x2 + 7x + 12 = (x + 3)(x + 4)

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**Note – If their product is negative one must be negative**

More difficult! Example Factorise x2 – 4x – 5 You are looking for two numbers a and b s.t. a + b = -4 and ab = -5 = -4 but 2 × -6 = -12 – No good = -4 and 1 × -5 = -5 – Great! Let a = 1 and b = -5 Therefore x2 – 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 x2 + 4x + 3**

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**Answers x2 + 4x + 3 = (x + 1)(x + 3) x2 + 8x + 15 = (x + 3)(x + 5)**

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© Boardworks Ltd 2005 1 of 73 Quadratics Stage 8 Chapter 18.

© Boardworks Ltd 2005 1 of 73 Quadratics Stage 8 Chapter 18.

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