# A1 Algebraic expressions

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A1 Algebraic expressions
KS3 Mathematics The aim of this unit is to teach pupils to: Use letter symbols and distinguish their different roles in algebra Know that algebraic operations follow the same conventions and order as arithmetic operations; use index notation and the index laws Simplify or transform algebraic expressions Material in this unit is linked to the Key Stage 3 Framework supplement of examples pp A1 Algebraic expressions

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

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)

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)

Algebraic multiplication square
Complete this activity as a group exercise. Use factorization to find the values of the missing terms across the top and along the side. Ask pupils how some of the multiplications could be written using brackets.

Pelmanism: Equivalent expressions
Work as a class to match equivalent expressions.