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Factorising quads diff 2 squares perfect squares

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Lesson that gives examples of how to factorise quadratic equations using the difference of 2 squares rule and the properties of perfect squares.

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• Factorising quads diff 2 squares perfect squares

1. 1. FACTORISING QUADRATICS Difference of 2 squares and Perfect Squares
2. 2. DIFFERENCE OF 2 SQUARES• Investigate (expand): (x − 5)(x + 5) = (x + 2)(x − 2) = (3x − 6)(3x + 6) =
3. 3. DIFFERENCE OF 2 SQUARES• Investigate (expand):(x − 5)(x + 5) =(x + 2)(x − 2) =(3x − 6)(3x + 6) =
4. 4. DIFFERENCE OF 2 SQUARES• Investigate (expand): 2 2(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25(x + 2)(x − 2) =(3x − 6)(3x + 6) =
5. 5. DIFFERENCE OF 2 SQUARES• Investigate (expand): 2 2(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25 2 2(x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4(3x − 6)(3x + 6) =
6. 6. DIFFERENCE OF 2 SQUARES• Investigate (expand): 2 2(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25 2 2(x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4 2(3x − 6)(3x + 6) = 9x + 18x − 18x − 36 2 = x − 36
7. 7. DIFFERENCE OF 2 SQUARES 2 2(a + b)(a − b) = a − b
8. 8. FACTORISING USING DIFFERENCE OF 2 SQUARES• Factorise 2 x −36
9. 9. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b• Factorise 2 x −36
10. 10. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 x −36
11. 11. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 x −36 a=x
12. 12. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 x −36 a=x b=6
13. 13. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 x −36 = (x + 6)(x − 6) a=x b=6
14. 14. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 4x −25
15. 15. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 4x −25 ( 2x ) −5 2 2
16. 16. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 4x −25 ( 2x ) −5 2 2a = 2x
17. 17. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 4x −25 ( 2x ) −5 2 2a = 2x b=5
18. 18. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 4x −25 = (2x + 5)(2x − 5) ( 2x ) −5 2 2a = 2x b=5
19. 19. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 3x −15
20. 20. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 3x −15 2( ) ( ) 2 3x − 15
21. 21. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 3x −15 2( ) ( ) 2 3x − 15a = 3x
22. 22. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 3x −15 2( ) ( ) 2 3x − 15a = 3x b = 15
23. 23. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b)• Factorise 2 3x −15 = ( 3x + 15 )( 3x − 15 ) 2( ) ( ) 2 3x − 15a = 3x b = 15
24. 24. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
25. 25. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
26. 26. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
27. 27. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
28. 28. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x b = −5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
29. 29. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x b = −5 2ab = 2 × x × (−5) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
30. 30. PERFECT SQUARES• Factorise 2 x − 8x + 16
31. 31. PERFECT SQUARES• Factorise 2 x − 8x + 16 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
32. 32. PERFECT SQUARES• Factorise 2 x − 8x + 16 a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
33. 33. PERFECT SQUARES• Factorise 2 x − 8x + 16 a=x b = −4 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
34. 34. PERFECT SQUARES• Factorise 2 x − 8x + 16 a=x b = −4 2ab = 2 × x × (−4) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
35. 35. PERFECT SQUARES• Factorise 2 2 x − 8x + 16 = (x − 4) a=x b = −4 2ab = 2 × x × (−4) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
36. 36. PERFECT SQUARES• Factorise 2 x + 2 5x + 5
37. 37. PERFECT SQUARES• Factorise 2 x + 2 5x + 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
38. 38. PERFECT SQUARES• Factorise 2 x + 2 5x + 5 a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
39. 39. PERFECT SQUARES• Factorise 2 x + 2 5x + 5 a=x b= 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
40. 40. PERFECT SQUARES• Factorise 2 x + 2 5x + 5 a=x b= 5 2ab = 2 × x × 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
41. 41. PERFECT SQUARES• Factorise 2 2 x + 2 5x + 5 = (x + 5 ) a=x b= 5 2ab = 2 × x × 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b