Cambridge International Mathematics

2 ANSWERS dcannot form a triangle 2 The sum of the lengths of any two sides of a triangle must be greater than the length of the ...

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Algebra (Expansion and factorisation) 1 Contents: A The distributive law [2.7] B The product(a+b)(c+d) [2.7] C Difference of two ...

32 Algebra (Expansion and factorisation) (Chapter 1) Consider the expression 2(x+3). We say that 2 is thecoefficientof the expre ...

Algebra (Expansion and factorisation) (Chapter 1) 33 i ¡2(x+4) j ¡3(2x¡1) k x(x+3) l 2 x(x¡5) m ¡3(x+2) n ¡4(x¡3) op¡2(x¡y) q a( ...

34 Algebra (Expansion and factorisation) (Chapter 1) Example 4 Self Tutor Expand and simplify: (2x+ 1)(3x¡2) (2x+ 1)(3x¡2) =2x£ ...

Algebra (Expansion and factorisation) (Chapter 1) 35 3 Expand and simplify: a (x+ 2)(x¡2) b (a¡5)(a+5) c (4 +x)(4¡x) d (2x+ 1)(2 ...

36 Algebra (Expansion and factorisation) (Chapter 1) Example 8 Self Tutor Expand and simplify: a (2x¡3)(2x+3) b (5¡ 3 y)(5 + 3y) ...

Algebra (Expansion and factorisation) (Chapter 1) 37 (a+b)^2 and (a¡b)^2 are calledperfect squares. Notice that (a+b)^2 =(a+b)(a ...

38 Algebra (Expansion and factorisation) (Chapter 1) Example 11 Self Tutor Expand and simplify: a (2x^2 +3)^2 b 5 ¡(x+2)^2 a (2x ...

Algebra (Expansion and factorisation) (Chapter 1) 39 In this section we expand more complicated expressions by repeated use of t ...

40 Algebra (Expansion and factorisation) (Chapter 1) b (x+ 1)(x¡3)(x+2) =(x^2 ¡ 3 x+x¡3)(x+2) fexpanding the first two factorsg ...

Algebra (Expansion and factorisation) (Chapter 1) 41 Example 15 Self Tutor Find the highest common factor of: a 8 aand 12 b b 4 ...

42 Algebra (Expansion and factorisation) (Chapter 1) Activity Algebraic common factor maze #endboxedheading To find your way thr ...

Algebra (Expansion and factorisation) (Chapter 1) 43 Example 17 Self Tutor Fully factorise: a 3 a+6 b ab¡ 2 bc 3 a+6 = 3 £a+ 3 £ ...

44 Algebra (Expansion and factorisation) (Chapter 1) EXERCISE 1G 1 Copy and complete: a 2 x+4=2(x+:::) b 3 a¡12 = 3(a¡:::) c 15 ...

Algebra (Expansion and factorisation) (Chapter 1) 45 We know theexpansionof (a+b)(a¡b) is a^2 ¡b^2. Thus, thefactorisationof a^2 ...

46 Algebra (Expansion and factorisation) (Chapter 1) Example 24 Self Tutor Factorise into linear factors: a x^2 ¡ 11 b (x+3)^2 ¡ ...

Algebra (Expansion and factorisation) (Chapter 1) 47 We know theexpansionof (x+a)^2 is x^2 +2ax+a^2 , so thefactorisationof x^2 ...

48 Algebra (Expansion and factorisation) (Chapter 1) Some expressions with four terms do not have an overall common factor, but ...