📚 Part A: Simplifying and Expanding

Instructions: Simplify each expression or expand the brackets. Show your working clearly.

1. Simplify: 3x + 5x - 2x

2. Simplify: 4a - 7 + 2a + 3

3. Expand: 3(2x + 5)

4. Expand: (x + 4)(x + 2)

5. Expand: (x - 3)(x + 7)

6. Expand: (2x + 1)(x - 4)

🔧 Part B: Factorising Quadratic Expressions

Instructions: Factorise each quadratic expression into two brackets.

7. Factorise: x² + 7x + 12

8. Factorise: x² - 5x + 6

9. Factorise: x² + 2x - 15

10. Factorise: x² - 9x + 20

Instructions: Solve each equation by factorising. Find all possible values of x.

11. Solve: x² + 5x + 6 = 0

12. Solve: x² - 7x + 12 = 0

Answers:

1. 6x 2. 6a - 4 3. 6x + 15 4. x² + 6x + 8

5. x² + 4x - 21 6. 2x² - 7x - 4 7. (x + 3)(x + 4)

8. (x - 2)(x - 3) 9. (x + 5)(x - 3) 10. (x - 4)(x - 5)

11. x = -2 or x = -3 12. x = 3 or x = 4