1. Expanding Brackets Multiply out and simplify

2. (x + 4) (x + 2) x2x2x2x2 = x 2 + 6x + 8 F O I L F  firsts O  outers I  inners L  lasts + 2x + 4x + 8 Now collect like terms

3. (2x + 1) (3x - 2) 6x26x26x26x2 = 6x 2 - x - 2 F O I L F  firsts O  outers I  inners L  lasts - 4x + 3x - 2 Now collect like terms

4. (3x - 4) (2x + 5) 6x26x26x26x2 = 6x 2 + 7x - 20 F O I L F  firsts O  outers I  inners L  lasts + 15x - 8x - 20 Now collect like terms

5. (x - 5) (4x - 3) 4x24x24x24x2 = 4x 2 - 23x + 15 F O I L F  firsts O  outers I  inners L  lasts - 3x - 20x + 15 Now collect like terms

6. 1. (x + 3)(x + 7)2. (x + 2)(x + 5) 3. (x + 9)(x + 3) Multiply out and simplify the following 4. (x – 5)(x – 6) 5. (x – 1)(x – 10)6. (x + 4)(x – 3) 7. (x – 7)(x + 2) 8. (x + 2)(x – 5) 9. (x – 3)(x + 8) x 2 + 10x + 21 x 2 + 7x + 15 x 2 + 12x + 27 x 2 - 11x + 30 x 2 - 11x + 10 x 2 + x - 12 x 2 - 5x - 14 x 2 - 3x - 10 x 2 + 5x - 24

7. 10. (2x + 3)(x + 1) 11. (x + 4)(3x + 2) 12. (2x + 7)(5x + 1) Multiply out and simplify the following 13. (2x – 5)(x – 2) 14. (3x – 1)(2x – 1) 15. (5x + 2)(x – 5) 16. (3x – 4)(2x + 9) 17. (4x + 1)(2x – 5) 18. (7x – 3)(2x + 3) 2x 2 + 5x + 3 3x 2 + 14x + 8 10x 2 + 37x + 7 2x 2 - 9x + 10 6x 2 - 5x + 1 5x 2 - 23x - 10 6x 2 + 19x - 36 8x 2 - 18x - 5 14x 2 + 15x - 9

8. Squaring Brackets

9. x2x2x2x2 = x 2 + 10x + 25 F O I L + 5x + 25 (x + 5) 2 = (x + 5) (x + 5) (x + 5) (x + 5) 52525252 x x xx x xx x xx x x 2 x (+5) x x)

10. x2x2x2x2 = x 2 - 10x + 25 F O I L - 5x + 25 (x - 5) 2 = (x - 5) (x - 5) (x - 5) (x - 5) 52525252 x x xx x xx x xx x x 2 x (-5) x x)

11. 9x29x29x29x2 = 9x 2 + 12x + 4 F O I L + 6x + 4 (3x - 2) 2 = (3x + 2) (3x + 2) 2 x (+2) x 3x) 22222222 3x x 3x3x x 3x3x x 3x3x x 3x (3x + 2) (3x + 2) (3x + 2) (3x + 2)

12. a2x2a2x2a2x2a2x2 = a 2 x 2 + 2abx + b 2 F O I L + abx + b 2 (ax + b) 2 = (ax + b) (ax + b) 2 x (+b) x ax) b2b2b2b2 ax x axax x axax x axax x ax (ax + b) (ax + b) (ax + b) (ax + b)

13. 1. (x + 3) 2 2. (x + 1) 2 3. (x + 9) 2 Multiply out using (ax + b) 2 = a 2 x 2 + 2abx + b 2 ) 4. (x – 6) 2 5. (x – 1) 2 6. (x + 4) 2 7. (x – 7) 2 8. (x + 2) 2 9. (x – 8) 2 x 2 + 6x + 9 x 2 + 2x + 1 x 2 + 18x + 81 x 2 - 12x + 36 x 2 - 2x + 1 x 2 + 8x + 16 x 2 - 14x + 49 x 2 + 4x + 4 x 2 - 16x + 64

14. 10. (2x + 3) 2 11. (5x + 1) 2 12. (4x + 9) 2 Multiply out using (ax + b) 2 = a 2 x 2 + 2abx + b 2 ) 13. (7x – 6) 2 14. (2x – 1) 2 15. (3x + 4) 2 16. (2x – 7) 2 17. (5x + 2) 2 18. (3x – 8) 2 4x 2 + 12x + 9 25x 2 + 10x + 1 16x 2 + 72x + 81 49x 2 - 84x + 36 4x 2 - 4x + 1 9x 2 + 24x + 16 4x 2 - 28x + 49 25x 2 + 20x + 4 9x 2 - 48x + 64