Quadratic Expressions Expanding Quadratic Expressions e g 1

Quadratic Expressions Expanding Quadratic Expressions e. g. 1 e. g. 2 A square of a quantity means multiply by itself

Quadratic Expressions Exercises 1. 2. 3. 4.

Quadratic Expressions Factorising Method 1: Common Factors e. g. means so, x is a factor of both terms. It is a common factor So, Common factor

Quadratic Expressions Exercises Factorise the following by taking out the common factors 1. 2. 3.

Quadratic Expressions 4. 5. 6. 7. 8.

Factorising Quadratic Expressions Method 2: The difference of two squares (Square roots) e. g. 1 A minus sign One square e. g. 2 Another square

Quadratic Expressions Exercises 1. 2. Common factor first! 3. Think! 4. What about Can’t do it! ? It’s NOT a difference

Factorising Quadratic Expressions Method 3: Trinomials e. g. 1 or The factors could not give 3 for the coefficient of x, so we try We need – 3 x so we want – 3 x is – 4 x and +1 x. called the linear term

Quadratic Expressions Method 3: Trinomials e. g. 2 Constant positive Signs of factors are the same

Quadratic Expressions Exercises Constant positive Signs of factors are the same 1. 2 3 2. 2 3 3. 3 4

Quadratic Expressions Exercises Constant negative Signs of factors are different 4. 1 6 5. 6 1 6. 1 3

Quadratic Expressions Exercises 7. 8. 9. 10. 11. 12.

SUMMARY Quadratic Expressions There are 3 methods of factorising quadratic expressions. Ø Common factors. Ø The difference of 2 squares. Ø Trinomial factors. • List possible pairs of factors of the constant. • Constant term positive signs are the same. • Constant term negative and one is negative. one sign is positive • Choose a pair of factors of the constant and check the linear term is correct. If not, try again.