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Breaking Brackets

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boyce
22 diapositives · 535 Views · Oct 23, 2014

Breaking Brackets. What is Factorisation. Factorise 3a + 3b. Examples. Interactive. 5a + 5. Interactive. 7g-21. 2d+8. 3e+15. Interactive. Interactive. 10a+5. 12b-3. Interactive. 8d-12. 4a+6. What is Factorisation. Factorisation is the opposite of multiplying. 6 is a factor of 12.

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

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

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

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

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

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

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

  8. 5a + 5b type Examples 3(r-s) 3r-3s a) 4(r-v) b) 4r-4v 9(r+w) 9r+9w c) 7(r+g) 7r+7g d) 0 2(r-h) Ans 2r-2h e) ( ) On (-) 6(s-v) h r 6s-6v f) C ² √ x 7 8 9 s 8(s+w) g) 8s+8w v 4 5 6 ÷ w 1 2 3 - 0 . = g Show Answers New Examples +

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

  10. 3a + 3 type Examples 4(b+1) 4b+4 a) 8(m+1) b) 8m+8 2(n-1) 2n-2 c) 6(v+1) 6v+6 d) 0 9(w+1) Ans 9w+9 e) ( ) On (-) 3(m+1) w a 3m+3 f) C ² √ x 7 8 9 b 7(n+1) g) 7n+7 m 4 5 6 ÷ n 1 2 3 - 0 . = v Show Answers New Examples +

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

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

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

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

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

  16. 4a + 12 type Examples 9w-81 a) b) 7p+28 2q+12 c) 3y-21 d) 0 Ans 4z-32 e) ( ) On (-) z v 6p-30 f) C ² √ x 7 8 9 w g) 8q+16 p 4 5 6 ÷ q 1 2 3 - 0 . = y Show Answers New Examples +

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

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

  19. 12b - 3 type Examples 5(9d+1) 45d+5 a) 4(3m+1) b) 12m+4 6(2n-1) 12n-6 c) 8(6e+1) 48e+8 d) 0 3(4f+1) Ans 12f+3 e) ( ) On (-) 2(8m+1) f c 16m+2 f) C ² √ x 7 8 9 d 9(5n-1) g) 45n-9 m 4 5 6 ÷ n 1 2 3 - 0 . = e Show Answers New Examples +

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

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

  22. No Multiple Examples 10(4s+3) 40s+30 a) 3(4y+3) b) 12y+9 5(2z-3) 10z-15 c) 6(4g-3) 24g-18 d) 0 5(5h-4) Ans 25h-20 e) ( ) On (-) 4(2y-5) h r 8y-20 f) C ² √ x 7 8 9 s 6(3z+4) g) 18z+24 y 4 5 6 ÷ z 1 2 3 - Start New Examples 0 . = g Show Answers +