Factorising quads diff 2 squares perfect squares
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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.

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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Transcript

  • 1. FACTORISING QUADRATICS Difference of 2 squares and Perfect Squares
  • 2. DIFFERENCE OF 2 SQUARES• Investigate (expand): (x − 5)(x + 5) = (x + 2)(x − 2) = (3x − 6)(3x + 6) =
  • 3. DIFFERENCE OF 2 SQUARES• Investigate (expand):(x − 5)(x + 5) =(x + 2)(x − 2) =(3x − 6)(3x + 6) =
  • 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. 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. 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. DIFFERENCE OF 2 SQUARES 2 2(a + b)(a − b) = a − b
  • 8. FACTORISING USING DIFFERENCE OF 2 SQUARES• Factorise 2 x −36
  • 9. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b• Factorise 2 x −36
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
  • 25. PERFECT SQUARES• Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
  • 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. 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. 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. 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. PERFECT SQUARES• Factorise 2 x − 8x + 16
  • 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. 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. 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. 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. 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. PERFECT SQUARES• Factorise 2 x + 2 5x + 5
  • 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. 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. 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. 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. 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