1. Breaking Brackets What is Factorisation Factorise 3a + 3b 5a + 5 ExamplesInteractive 2d+8 3e+15 7g-21 Interactive 10a+512b-3 Interactive 4a+6 8d-12 Interactive

2. What is Factorisation Factorisation is the opposite of multiplying. 12 = 6 x 2 6 is a factor of 12 2 is a factor of 12 When you factorise you produce a multiplication sum 12 = 1 x 1212 = 2 x 6 12 = 3 x 4 The factorisations we normally do in Maths involve letters 3a = 3 x a5f = 5 x f 7k = 7 x kab = a x b

3. Factorise 3a + 3b a a a 3a b b b 3b a + b Three rows with ( a + b ) in each row. The Maths code is 3 ( a + b ) 3a + 3b = 3 ( a + b )

4. Factorise 7d + 7g d d d 7d g g g 7g d + g Seven rows with ( d + g ) in each row. The Maths code is 7 ( d + g ) 7d + 7g = 7 ( d + g ) d g d g d g d g d + g

5. Factorise 8c + 8d Factorisation is the opposite of multiplying. In this case a term = 8 x c = 8d Take each term and put time signs between numbers and letters + 8c x ()………… by a single bracket 8c 8d Find the HCF of both numbers In this case both numbers are the same. The HCF is 8. + From the previous examples you probably know that 8c + 8d = A method follows 8 ( c + d ) 8 x d

6. Factorisation Opposite of Multiplying a Bracket 8 c + 8 d ( ) = + Put in brackets and one arrow for each term Both terms contain 8 so the common factor is x x 8 8 8c = 8 x c c 8d = 8 x 8c =8 x c 8c d d What do you multiply 8 by to get the two terms Copy down the sign Put 8 at the front of the brackets 8 8 8c =8 x d 8d

7. More Examples 9 ( ) 5 ( ) 2 x + 2y = x + y 2 ( ) 9p + 9q = p + q 5a + 5e = a + e 3 ( ) 3s – 3t = s - t 11 ( ) 11y – 11t = y - t 12 ( ) 12g – 12w = g - w Examples (a) 7f + 7k (b) 2h + 2j (c) 5t – 5u (d) 14g – 14k (e) 26b + 26v Factorise =7(f + k ) =2(h + j ) =5(t - u ) =14(g - k ) =26(b + v )

8. 5a + 5b type Examples a) b) c) d) e) f) g) 3r-3s 3(r-s) 4r-4v 9r+9w 7r+7g 2r-2h 6s-6v 8s+8w 4(r-v) 9(r+w) 7(r+g) 2(r-h) 6(s-v) 8(s+w) 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) r New Examples Show Answers s v w g h ( )

9. Factorise 5a + 5 5a + 5 ( ) = + Put in brackets and one arrow for each term Both terms contain 5 so the common factor is x x 5 5 5a = 5 x a a 5 = 5 x 1 1 What do you multiply 5 by to get the two terms Copy down the sign Put 5 at the front of the brackets 5 5

10. 3a + 3 type Examples a) b) c) d) e) f) g) 4b+4 4(b+1) 8m+8 2n-2 6v+6 9w+9 3m+3 7n+7 8(m+1) 2(n-1) 6(v+1) 9(w+1) 3(m+1) 7(n+1) 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) a New Examples Show Answers b m n v w ( )

11. How to Factorise 2d + 8 8 + 2 d ( ) = + x x Factorising is the opposite of multiplying the contents of a bracket + by a number ( or a term ) Need to find a number that you can multiply something to get 2d and 8. Find a common factor

12. How to Factorise 2d + 8 8 + 2 d ( ) = + x x 2 2 + 2d is one term 8 is the 2 nd term Concentrate on the number part of each … 2 and 8 2d 2 x d 8 2 x 4 2 d 4 2 is a COMMON FACTOR of 2d and 8

13. In rows d d 2d2d 4 4 8 d + 4 2 d + 8 = 2 ( d + 4 ) Two rows with ( d + 4 ) in each row. The Maths code is 2 ( d + 4 )

14. How to Factorise 3e + 15 15 + 3e ( ) = + x x 3 3 + 3 e 5 3 is a COMMON FACTOR of 3e and 15 Numbers 3 and 15 3 x 5 = 15 3 x e+3 x 5

15. How to Factorise 7g - 21 21 - 7g ( ) = - x x 7 7 - 7 e 3 7 is a COMMON FACTOR of 7g and 21 Numbers 7 and 21 7 x 3 = 21 7 x g+7 x 3 **** - between 7g and 21 - in brackets ***********

16. 4a + 12 type Examples a) b) c) d) e) f) g) 9w-81 7p+28 2q+12 3y-21 4z-32 6p-30 8q+16 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) v New Examples Show Answers w p q y z ( )

17. How to Factorise 10a + 5 5 + 10a ( ) = x x 5 5 + 5 2a 1 5 is a COMMON FACTOR of 10a and 5 Numbers 10 and 5 5 x 2 = 10 5 x 2 x a+5 x 1 10a 5 5 x 2 = 10 …… don’t want 10 want 10a 5 x 2a = 10a

18. How to Factorise 12b - 3 3 - 12b ( ) = x x 3 3 - 3 4b 1 3 is a COMMON FACTOR of 12b and 3 Numbers 12 and 3 3 x 4 = 12 3 x 4 x b-3 x 1 12b 3 3 x 4 = 12 …… don’t want 12 want 12b 3 x 4b = 12b

19. 12b - 3 type Examples a) b) c) d) e) f) g) 45d+5 5(9d+1) 12m+4 12n-6 48e+8 12f+3 16m+2 45n-9 4(3m+1) 6(2n-1) 8(6e+1) 3(4f+1) 2(8m+1) 9(5n-1) 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) c New Examples Show Answers d m n e f ( )

20. How to Factorise 4a + 6 6 + 4a ( ) = x x 2 2 + 2 2a 3 2 is a COMMON FACTOR of 4a and 6 Numbers 4 and 6 4 x = 6 2 x 2 x a+2 x 3 4a 6 What times table are 4 and 6 both in 2 x 2 = 4 2 x 3 = 6

21. How to Factorise 8d - 12 12 - 8d ( ) = x x 4 4 - 4 2d 3 4 is a COMMON FACTOR of 8d and 12 Numbers 8 and 12 8 x = 12 4 x 2 x d-4 x 3 8d 12 What times table are 8 and 12 both in 2 x 4 = 82 x 6 = 12 4 x 2 = 84 x 3 = 12

22. No Multiple Examples a) b) c) d) e) f) g) 40s+30 10(4s+3) 12y+9 10z-15 24g-18 25h-20 8y-20 18z+24 3(4y+3) 5(2z-3) 6(4g-3) 5(5h-4) 4(2y-5) 6(3z+4) 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) r New Examples Show Answers s y z g h ( ) Start