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© Boardworks Ltd of 60 KS3 Mathematics A1 Algebraic expressions

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© Boardworks Ltd of 60 A1.5 Factorizing expressions Contents A1 Algebraic expressions A1.1 Writing expressions A1.3 Multiplying terms A1.2 Collecting like terms A1.4 Dividing terms A1.6 Substitution

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© Boardworks Ltd of 60 Factorizing expressions Some expressions can be simplified by dividing each term by a common factor and writing the expression using brackets. For example, in the expression 5 x + 10 the terms 5 x and 10 have a common factor, 5. We can write the 5 outside of a set of brackets 5( x + 2) We can write the 5 outside of a set of brackets and mentally divide 5 x + 10 by 5. (5 x + 10) ÷ 5 = x + 2 This is written inside the bracket. 5( x + 2)

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© Boardworks Ltd of 60 Factorizing expressions Writing 5 x + 10 as 5( x + 2) is called factorizing the expression. Factorize 6 a a + 8 =2(3 a + 4) Factorize 12 – 9 n 12 – 9 n =3(4 – 3 n ) The highest common factor of 6a and 8 is 2.2. (6 a + 8) ÷ 2 =3 a + 4 The highest common factor of 12 and 9 n is 3.3. (12 – 9 n ) ÷ 3 =4 – 3 n

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© Boardworks Ltd of 60 Factorizing expressions Writing 5 x + 10 as 5( x + 2) is called factorizing the expression. 3 x + x 2 = x (3 + x ) 2 p + 6 p 2 – 4 p 3 = 2 p (1 + 3 p – 2 p 2 ) The highest common factor of 3 x and x 2 is x.x. (3 x + x 2 ) ÷ x =3 + x The highest common factor of 2 p, 6 p 2 and 4 p 3 is 2p.2p. (2 p + 6 p 2 – 4 p 3 ) ÷ 2 p = p – 2 p 2 Factorize 3 x + x 2 Factorize 2 p + 6 p 2 – 4 p 3

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© Boardworks Ltd of 60 Algebraic multiplication square

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© Boardworks Ltd of 60 Pelmanism: Equivalent expressions

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