5) 4a + 3b = 22 6) 3p + 3q = 15 5a 4b = 43 2p + 5q = 14 – Chapter 4: FACTORISING Common factors We can factorise some expressions by taking out a common factor. Example 1: Factorise 12x 30 – Solution: 6 is a common factor to both 12 and 30. We can therefore factorise by taking 6 outside a bracket: 12x 30 = 6(2x 5) – – Example 2: Factorise 6x2 2xy – Solution: 2 is a common factor to both 6 and 2. Both terms also contain an x. So we factorise by taking 2x outside a bracket. 6x2 2xy = 2x(3x y) – – Example 3: Factorise 9x3y2 18x2y – 9 is a common factor to both 9 and 18. Solution: The highest power of that is present in both expressions is x x2. There is also a present in both parts. y So we factorise by taking 9x2y outside a bracket: 9x3y2 18x2y = 9x2y(xy 2) – – Example 4: Factorise 3x(2x 1) 4(2x 1) – – –
5) 4a + 3b = 22 6) 3p + 3q = 15 5a – 4b = 43 2p + 5q = 14 Chapter 4: FACTORISING Common factors We can factorise some expressions by taking out a common factor. Example 1: Factorise 12x – 30 Solution: 6 is a common factor to both 12 and 30. We can therefore factorise by taking 6 outside a bracket: 12x – 30 = 6(2x – 5) Example 2: Factorise 6x2 – 2xy Solution: 2 is a common factor to both 6 and 2. Both terms also contain an x. So we factorise by taking 2x outside a bracket. 6x2 – 2xy = 2x(3x – y) Example 3: Factorise 9x3y2 – 18x2y Solution: 9 is a common factor to both 9 and 18. The highest power of x that is present in both expressions is x2. There is also a y present in both parts. So we factorise by taking 9x2y outside a bracket: 9x3y2 – 18x2y = 9x2y(xy – 2) Example 4: Factorise 3x(2x – 1) – 4(2x – 1)
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