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Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. By expanding brackets we mean multiply each term in the bracket by the term outside. 5(2x + 3) means 5 x (2x + 3) 5(2x + 3) = 10x + 15 Example 1 Expand 3(x + 5) = 3x + 15 Example 2 Expand 4(3x - 2) = 12x - 8 Intro Brackets

Questions 1 Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. Expand each of the following: (a) 3x + 24 (b) 7x + 14 (c) 10x - 4 (d) 16x - 24 (e) 7y + 7 (f) 27k - 72 (a) 3(x + 8) (b) 7(x + 2) (c) 2(5x - 2) (d) 8(2x - 3) (e) 7(y + 1) (f) 9(3k - 8)

Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. Once negative signs are introduced we need to be mindful of the rules for signs when multiplying. + x + = + + x - = - - x + = - - x - = +- x - = + Like signs  PLUS, Unlike signs  MINUS Example 3 Expand -2(x + 3) = -2x - 6 Example 4 Expand 3(3x - 1) = 9x - 3 Example 5 Expand -5(-x + 3) = 5x - 15 Example 6 Expand 7(-2x - 3) = -14x - 21

Questions 2 Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. Expand each of the following: (a) -3x - 24 (b) -7x + 14 (c) -10x - 4 (d) 16x + 8 (e) -7y - 7 (f) -27k - 72 (a) -3(x + 8) (b) 7(-x + 2) (c) 2(-5x - 2) (d) -8(-2x - 1) (e) -7(y + 1) (f) 9(-3k - 8)

Simplifying Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. + x + = + + x - = - - x + = - - x - = +- x - = + Simplifying Expressions Involving Brackets Example 1: Expand and simplify the expression: 7(x + 5) + 3(x + 4) 7x + 35 + 3x + 12 10x + 47 expand each bracket collect like terms Example 2: Expand and simplify the expression: 8(x + 1) - 5(x + 2) 8x + 8 - 5x - 10 3x - 2 expand each bracket collect like terms

Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. + x + = + + x - = - - x + = - - x - = +- x - = + Simplifying Expressions Involving Brackets Example 3: Expand and simplify the expression: 2(x - 1) - 3(x - 4) 2x - 2 - 3x + 12 - x + 10 or 10 - x expand each bracket collect like terms Example 4: Expand and simplify the expression: 9 x - 2(3x - 8) + 3(x - 2) - 4(x - 1) - 5 9x - 6x + 16 + 3x - 6 - 4x + 4 - 5 2x + 9 expand each bracket collect like terms

Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. Expand and simplify each of the following: (a) 7x + 26 (b) 5x - 1 (c) 17x - 8 (d) 16 - 9x (e) 10x + 19 (f) x - 25 (a) 4(x + 5) + 3(x + 2) (b) 2(3x + 1) - (x + 3) (c) 3(5x - 2) + 2(x - 1) (d) -7(x - 2) - 2(x - 1) (e) 5(3x - 1) - 4(2x - 3) + 3(x + 4) (f) 9 + 2(5x - 3) - 7(2x + 4) + 5x Questions 3

Intro Factorising Brackets and Factorising In algebra we often need to simplify expressions and this may involve expanding/removing brackets as well as factorising. By expanding brackets we mean multiply each term in the bracket by the term outside. 4(2x + 3) means 4 x (2x + 3) 4(2x + 3) =8x + 12 Factorising Expressions Factorising is simply the reverse of expanding brackets. To factorise an expression completely, we take the highest common factor (HCF) of each term and place this outside the bracket. 6x + 24 Example Question: Choose the option below that gives a complete factorisation of: (a) 2(3x + 12) (b) 3(2x + 8) (c) 6(x + 4)

Brackets and Factorising Factorising Expressions Example Question 1: Factorise the following expression: 3x + 3 3(x + 1) HCF = 3 Example Question 2: Factorise the following expression: 8x - 20 4(2x - 5) HCF = 4 Example Question 3: Factorise the following expression: 21x - 28 7(3x - 4) HCF = 7 Factorising is simply the reverse of expanding brackets. To factorise an expression completely, we take the highest common factor (HCF) of each term and place this outside the bracket. + x + = + + x - = - - x + = - - x - = +- x - = +

Questions 4 Brackets and Factorising Factorise each of the following: (a) 4(x + 2) (a) 4x + 8 (b) 6x + 27 (c) 15x - 18 (d) 40 + 16x (e) 20p - 25 (f) 8x + 12y - 20 Factorising Expressions Factorising is simply the reverse of expanding brackets. To factorise an expression completely, we take the highest common factor (HCF) of each term and place this outside the bracket. (b) 3(2x + 9) (c) 3(5x - 6) (d) 8(2x + 5) (e) 5(4p - 5) (f) 4(2x + 3y - 5)

Worksheet (a) 3(x + 8) (b) 7(x + 2) (c) 2(5x - 2) (d) 8(2x - 3) (e) 7(y + 1) (f) 9(3k - 8) 1 (a) -3(x + 8) (b) 7(-x + 2) (c) 2(-5x - 2) (d) -8(-2x - 1) (e) -7(y + 1) (f) 9(-3k - 8) 2 (a) 4(x + 5) + 3(x + 2) (b) 2(3x + 1) - (x + 3) (c) 3(5x - 2) + 2(x - 1) (d) -7(x - 2) - 2(x - 1) (e) 5(3x - 1) - 4(2x - 3) + 3(x + 4) (f) 9 + 2(5x - 3) - 7(2x + 4) + 5x 3 (a) 4x + 8 (b) 6x + 27 (c) 15x - 18 (d) 40 + 16x (e) 20p - 25 (f) 8x + 12y - 20 4 Worksheet 1