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KS3 Mathematics

KS3 Mathematics. A1 Algebraic expressions. Contents. A1 Algebraic expressions. A1.1 Writing expressions. A1.2 Collecting like terms. A1.3 Multiplying terms. A1.4 Dividing terms. A1.5 Factorizing expressions. A1.6 Substitution. Factorizing expressions.

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KS3 Mathematics

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  1. KS3 Mathematics A1 Algebraic expressions

  2. Contents A1 Algebraic expressions A1.1 Writing expressions A1.2 Collecting like terms A1.3 Multiplying terms A1.4 Dividing terms A1.5 Factorizing expressions A1.6 Substitution

  3. 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 5x + 10 the terms 5x and 10 have a common factor, 5. We can write the 5 outside of a set of brackets We can write the 5 outside of a set of brackets and mentally divide 5x + 10 by 5. (5x + 10) ÷ 5 = x + 2 This is written inside the bracket. 5(x+ 2) 5(x+ 2)

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

  5. Factorizing expressions Writing 5x + 10 as 5(x + 2) is called factorizing the expression. Factorize 3x + x2 Factorize 2p + 6p2 – 4p3 The highest common factor of 3x and x2 is The highest common factor of 2p, 6p2 and 4p3 is x. 2p. (2p + 6p2 – 4p3) ÷ 2p = (3x + x2) ÷ x = 3 + x 1 + 3p – 2p2 3x + x2 = x(3 + x) 2p + 6p2 – 4p3 = 2p(1 + 3p – 2p2)

  6. Algebraic multiplication square

  7. Pelmanism: Equivalent expressions

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